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Journal articles on the topic 'Hamiltonian equivalence'

Author: Grafiati

Published: 10 March 2023

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1

Qian, Jing, Yun Zeng, Li Xiang Zhang, and Tian Mao Xu. "Analysis on Equivalence between Transfer Function and Equivalent Circuit Simulation in General Hamiltonian Modeling." Applied Mechanics and Materials 204-208 (October 2012): 4896–99. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.4896.

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Take generator system included AVR (automatic voltage regulator) and PSS (power system stabilizer) as an example, Using the time simulation method, Study the equivalence between the transfer function model and the equivalent circuit simulation, and establish the corresponding relations between the circuit structures, internal parameters and transfer function parameters, based on the energy of equivalent circuit, the Hamiltonian function of transfer function is derived indirectly, and the Hamiltonian model is established. The study in this paper provides a new way to establish generalized Hamil

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2

Nikitin, A. G., and V. V. Tretynyk. "Parasupersymmetries and Non-Lie Constants of Motion for Two-Particle Equations." International Journal of Modern Physics A 12, no. 24 (1997): 4369–86. http://dx.doi.org/10.1142/s0217751x97002371.

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We search for hidden symmetries of two-particle equations with oscillator-equivalent potential, proposed by Moshinsky with collaborators. We proved that these equations admit hidden symmetries and parasupersymmetries which enable one to easily find the Hamiltonian spectra using algebraic methods and to construct exact Foldy–Wouthuysen transformations. Moreover, we demonstrate that these equations are reducible and generate Hamiltonians for pararelativistic or Kemmer oscillators. We also establish equivalence relations between different approaches to Kemmer oscillator and propose new one- and t

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3

DERIGLAZOV, A. A., W. OLIVEIRA, and G. OLIVEIRA-NETO. "EQUIVALENCE BETWEEN DIFFERENT CLASSICAL TREATMENTS OF THE O(N) NONLINEAR SIGMA MODEL AND THEIR FUNCTIONAL SCHRÖDINGER EQUATIONS." International Journal of Modern Physics A 18, no. 05 (2003): 755–66. http://dx.doi.org/10.1142/s0217751x03013867.

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In this work we derive the Hamiltonian formalism of the O(N) nonlinear sigma model in its original version as a second-class constrained field theory and then as a first-class constrained field theory. We treat the model as a second-class constrained field theory by two different methods: the unconstrained and the Dirac second-class formalisms. We show that the Hamiltonians for all these versions of the model are equivalent. Then, for a particular factor-ordering choice, we write the functional Schrödinger equation for each derived Hamiltonian. We show that they are all identical which justifi

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4

Balajany, Hamideh, and Mohammad Mehrafarin. "Geometric phase of cosmological scalar and tensor perturbations in f(R) gravity." Modern Physics Letters A 33, no. 14 (2018): 1850077. http://dx.doi.org/10.1142/s0217732318500773.

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By using the conformal equivalence of f(R) gravity in vacuum and the usual Einstein theory with scalar-field matter, we derive the Hamiltonian of the linear cosmological scalar and tensor perturbations in f(R) gravity in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes as a Lewis–Riesenfeld phase.

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5

M, Nandakumar, and K. S. Subrahamanian Moosath. "Rough Liouville Equivalence of Integrable Hamiltonian Systems." Advances in Dynamical Systems and Applications 15, no. 2 (2020): 153–69. http://dx.doi.org/10.37622/adsa/15.2.2020.153-169.

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6

Nirov, Kh S., and A. V. Razumov. "Equivalence between Lagrangian and Hamiltonian BRST formalisms." Journal of Mathematical Physics 34, no. 9 (1993): 3933–53. http://dx.doi.org/10.1063/1.530410.

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7

Martynchuk, N. N. "Semi-local Liouville equivalence of complex Hamiltonian systems defined by rational Hamiltonian." Topology and its Applications 191 (August 2015): 119–30. http://dx.doi.org/10.1016/j.topol.2015.05.090.

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8

AMICO, LUIGI. "ALGEBRAIC EQUIVALENCE BETWEEN CERTAIN MODELS FOR SUPERFLUID–INSULATOR TRANSITION." Modern Physics Letters B 14, no. 21 (2000): 759–66. http://dx.doi.org/10.1142/s0217984900000963.

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Algebraic contraction is proposed to realize mappings between Hamiltonian models. This transformation contracts the algebra of the degrees of freedom underlying the Hamiltonian. The rigorous mapping between the anisotropic XXZ Heisenberg model, the quantum phase model and the Bose Hubbard model is established as the contractions of the algebra u(2) underlying the dynamics of the XXZ Heisenberg model.

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9

Cheng, Daizhan, Alessandro Astolfi, and Romeo Ortega. "On feedback equivalence to port controlled Hamiltonian systems." Systems & Control Letters 54, no. 9 (2005): 911–17. http://dx.doi.org/10.1016/j.sysconle.2005.02.005.

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10

Salat, A. "Hamiltonian Approach to Magnetic Fields with Toroidal Surfaces." Zeitschrift für Naturforschung A 40, no. 10 (1985): 959–67. http://dx.doi.org/10.1515/zna-1985-1001.

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The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail.Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to

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11

NIROV, KH S., and A. V. RAZUMOV. "FIELD-ANTIFIELD AND BFV FORMALISMS FOR QUADRATIC SYSTEMS WITH OPEN GAUGE ALGEBRAS." International Journal of Modern Physics A 07, no. 23 (1992): 5719–38. http://dx.doi.org/10.1142/s0217751x9200260x.

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The Lagrangian field-antifield (BV) and Hamiltonian (BFV) BRST formalisms for the general quadratic systems with open gauge algebra are considered. The equivalence between the Lagrangian and Hamiltonian formalisms is proven.

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12

BERING, K. "FROM HAMILTONIAN TO LAGRANGIAN Sp(2) BRST QUANTIZATION." Modern Physics Letters A 11, no. 06 (1996): 499–513. http://dx.doi.org/10.1142/s0217732396000540.

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We give a formal proof of the equivalence of Hamiltonian and Lagrangian BRST quantization. This is done for a generic Sp(2)-symmetric theory using flat (Darboux) coordinates. A new quantum master equation is derived in a Hamiltonian setting which contains all the Hamiltonian fields and momenta of a given theory.

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13

Zhu, W. Q., T. T. Soong, and Y. Lei. "Equivalent Nonlinear System Method for Stochastically Excited Hamiltonian Systems." Journal of Applied Mechanics 61, no. 3 (1994): 618–23. http://dx.doi.org/10.1115/1.2901504.

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An equivalent nonlinear system method is presented to obtain the approximate probability density for the stationary response of multi-degree-of-freedom nonlinear Hamiltonian systems to Gaussian white noise parametric and/or external excitations. The equivalent nonlinear systems are obtained on the basis of one of the following three criteria: least mean-squared deficiency of damping forces, dissipation energy balancing, and least mean-squared deficiency of dissipation energies. An example is given to illustrate the application and validity of the method and the differences in the three equival

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14

YOKOMICHI, Masahiro, and Masasuke SHIMA. "Equivalence and Normal Form for Nonlinear Hamiltonian Control Systems." Transactions of the Society of Instrument and Control Engineers 30, no. 6 (1994): 609–16. http://dx.doi.org/10.9746/sicetr1965.30.609.

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15

Chang, Dong Eui, Anthony M. Bloch, Naomi E. Leonard, Jerrold E. Marsden, and Craig A. Woolsey. "The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems." ESAIM: Control, Optimisation and Calculus of Variations 8 (2002): 393–422. http://dx.doi.org/10.1051/cocv:2002045.

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16

Ahlbrandt, C. D. "Equivalence of Discrete Euler Equations and Discrete Hamiltonian Systems." Journal of Mathematical Analysis and Applications 180, no. 2 (1993): 498–517. http://dx.doi.org/10.1006/jmaa.1993.1413.

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17

WEITZMAN, MARTIN L. "The linearised Hamiltonian as comprehensive NDP." Environment and Development Economics 5, no. 1 (2000): 55–68. http://dx.doi.org/10.1017/s1355770x0000005x.

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For guidance in determining which items should be included in comprehensive NDP (net domestic product) and how they should be included, reference is often made to the linearised Hamiltonian from an optimal growth problem. The paper gives a rigorous interpretation of this procedure in terms of a money-metric utility function linked to familiar elements of standard welfare theory. A key insight is that the Hamiltonian itself is a quasilinear utility function, so imposing the money-metric normalisation is simply equivalent to using Marshallian consumer surplus as the appropriate measure of welfar

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18

BATALIN, I. A., and I. V. TYUTIN. "ON THE PERTURBATIVE EQUIVALENCE BETWEEN THE HAMILTONIAN AND LAGRANGIAN QUANTIZATIONS." International Journal of Modern Physics A 11, no. 08 (1996): 1353–66. http://dx.doi.org/10.1142/s0217751x96000626.

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The Hamiltonian (BFV) and Lagrangian (BV) quantization schemes are proved to be perturbatively equivalent to each other. It is shown in particular that the quantum master equation being treated perturbatively possesses a local formal solution.

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19

Zhu, W. Q., and Y. Lei. "Equivalent Nonlinear System Method for Stochastically Excited and Dissipated Integrable Hamiltonian Systems." Journal of Applied Mechanics 64, no. 1 (1997): 209–16. http://dx.doi.org/10.1115/1.2787275.

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An equivalent nonlinear system method is proposed to obtain the approximate probability density for the stationary response of multi-degree-of-freedom integrable Hamiltonian systems with linear and (or) nonlinear dampings and subject to external and (or) parametric excitations of Gaussian white noises. The equivalent nonlinear systems are obtained on the basis of one of the following three criteria: least mean-squared difference in damping forces, dissipation energy balancing, or least mean-squared difference in dissipation energies. Two examples are given to illustrate the application and val

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20

Accardi, Luigi, and Wided Ayed. "Free white noise flows." Infinite Dimensional Analysis, Quantum Probability and Related Topics 20, no. 03 (2017): 1750014. http://dx.doi.org/10.1142/s021902571750014x.

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We extend to free white noise Heisenberg equations the proof of the equivalence between (non-Hamiltonian) stochastic differential equations and Hamiltonian white noise equations. This gives in particular, the microscopic structure of the maps defining free white noise stochastic flows in terms of the free white noise derivations defining them.

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21

Sk, Nayem, and Abhik Kumar Sanyal. "Why scalar–tensor equivalent theories are not physically equivalent?" International Journal of Modern Physics D 26, no. 14 (2017): 1750162. http://dx.doi.org/10.1142/s0218271817501620.

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Whether Jordan’s and Einstein’s frame descriptions of [Formula: see text] theory of gravity are physically equivalent, is a long standing debate. However, practically none questioned on true mathematical equivalence, since classical field equations may be translated from one frame to the other following a transformation relation. Here, we show that, neither Noether symmetries, Noether equations, nor may quantum equations be translated from one to the other. The reason being, — conformal transformation results in a completely different system, with a different Lagrangian. Field equations match

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22

TAO, R. B., X. HU, and M. SUZUKI. "DISCUSSION ON THE MEAN FIELD APPROXIMATION IN THE RVB THEORY." Modern Physics Letters B 02, no. 10 (1988): 1205–9. http://dx.doi.org/10.1142/s0217984988001144.

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Baskaran’s mean field approximation of the Hubbard Hamiltonian with strong correlation and half-filling is discussed. Our calculations show that his decoupling of the Hamiltonian is not permissible in the half-filling case and that it destroys the equivalence of the Hubbard model to the Heisenberg magnetic system and violates some spin-spin relations.

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23

Grigoryan, G. V., R. P. Grigoryan, and I. V. Tyutin. "Equivalence of lagrangian and hamiltonian BRST quantizations: the general case." Nuclear Physics B 379, no. 1-2 (1992): 304–18. http://dx.doi.org/10.1016/0550-3213(92)90598-6.

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24

Passerini, A., M. Bregola, G. Callegari, and C. Ferrario. "Infinitesimal transformations and equivalence of the Lagrangian and Hamiltonian descriptions." European Journal of Physics 14, no. 5 (1993): 211–16. http://dx.doi.org/10.1088/0143-0807/14/5/004.

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25

Batlle, C., J. Gomis, J. M. Pons, and N. Roman‐Roy. "Equivalence between the Lagrangian and Hamiltonian formalism for constrained systems." Journal of Mathematical Physics 27, no. 12 (1986): 2953–62. http://dx.doi.org/10.1063/1.527274.

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26

GOVAERTS, JAN. "HAMILTONIAN REDUCTION OF FIRST-ORDER ACTIONS." International Journal of Modern Physics A 05, no. 18 (1990): 3625–40. http://dx.doi.org/10.1142/s0217751x90001574.

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The Hamiltonian structure associated to an arbitrary system described by a first-order action is considered in detail. The equivalence of two possible approaches is established in full generality. The first has been advocated recently by Faddeev and Jackiw. The second is based on the more standard methods of constrained dynamics. Some consequences of the general analysis are also discussed.

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27

SHAFIEE, M. "ON HAMILTONIAN GROUP OF MULTISYMPLECTIC MANIFOLDS." International Journal of Geometric Methods in Modern Physics 08, no. 05 (2011): 929–35. http://dx.doi.org/10.1142/s0219887811005506.

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In this paper the Hamiltonian group Ham (M, Ω) is defined for a compact k-plectic manifold (M, Ω) and it is shown that its Lie algebra is the space of equivalence classes of Hamiltonian forms, modulo closed forms. Also if ψ be a multisymplectomorphism in the identity component Msymp 0(M, Ω) of the group of multisymplectomorphisms Msymp (M, Ω), we obtain a necessary and sufficient condition under which ψ belongs to Ham (M, Ω). As two consequences, we show that Hamiltonian paths are generated by Hamiltonian forms and if Hk (M, ℝ) = 0, then Ham (M, Ω) is equal to Msymp 0(M, Ω).

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28

ECHEVERRÍA ENRÍQUEZ, A., M. C. MUÑOZ LECANDA, and N. ROMÁN ROY. "GEOMETRICAL SETTING OF TIME-DEPENDENT REGULAR SYSTEMS: ALTERNATIVE MODELS." Reviews in Mathematical Physics 03, no. 03 (1991): 301–30. http://dx.doi.org/10.1142/s0129055x91000114.

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We analyse exhaustively the geometric formulations of the time-dependent regular dynamical systems, both the Hamiltonian and the Lagrangian formalisms. We study the equivalence between the different models and, in each case, between the Lagrangian and the Hamiltonian formulations, giving the suitable definitions of the Legendre transformation. In addition, we include the variational formalisms as well as the Klein formalism.

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29

BANERJEE, RABIN, BISWAJIT CHAKRABORTY, and TOMY SCARIA. "POLARIZATION VECTORS AND DOUBLET STRUCTURE IN PLANAR FIELD THEORY." International Journal of Modern Physics A 16, no. 24 (2001): 3967–88. http://dx.doi.org/10.1142/s0217751x01005092.

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We establish the equivalence of the Maxwell–Chern–Simons–Proca model to a doublet of Maxwell–Chern–Simons models defined in a variety of covariant gauges. This equivalence is shown to hold at the level of polarization vectors of the basic fields. The analysis is done in both Lagrangian and Hamiltonian formalisms and compatible results are obtained. A similar equivalence with a doublet of self and anti-self dual models is briefly discussed.

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30

de León, Manuel, and Manuel Lainz Valcázar. "Singular Lagrangians and precontact Hamiltonian systems." International Journal of Geometric Methods in Modern Physics 16, no. 10 (2019): 1950158. http://dx.doi.org/10.1142/s0219887819501585.

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In this paper, we discuss the singular Lagrangian systems on the framework of contact geometry. These systems exhibit a dissipative behavior in contrast with the symplectic scenario. We develop a constraint algorithm similar to the presymplectic one studied by Gotay and Nester (the geometrization of the well-known Dirac–Bergmann algorithm). We also construct the Hamiltonian counterpart and prove the equivalence with the Lagrangian side. A Dirac–Jacobi bracket is constructed similar to the Dirac bracket.

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31

Popescu, Liviu. "Dual Structures on the Prolongations of a Lie Algebroid." Annals of the Alexandru Ioan Cuza University - Mathematics 59, no. 2 (2013): 373–90. http://dx.doi.org/10.2478/v10157-012-0037-4.

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Abstract In the present paper we study the properties of dual structures on the prolongations of a Lie algebroid. We introduce the dynamical covariant derivative on Lie algebroids and prove that the nonlinear connection induced by a regular Lagrangian is compatible with the metric and symplectic structures. The notions of mechanical structure and semi-Hamiltonian section are introduced on the prolongation of the Lie algebroid to its dual bundle and their properties are investigated. Finally, we prove the equivalence between the metric nonlinear connection and semi-Hamiltonian section, using th

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32

Martins, Ricardo Miranda. "Formal equivalence between normal forms of reversible and hamiltonian dynamical systems." Communications on Pure and Applied Analysis 13, no. 2 (2013): 703–13. http://dx.doi.org/10.3934/cpaa.2014.13.703.

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33

Dresse, Alain, Philippe Gregoire, and Marc Henneaux. "Path-integral equivalence between the extended and non-extended hamiltonian formalisms." Physics Letters B 245, no. 2 (1990): 192–96. http://dx.doi.org/10.1016/0370-2693(90)90132-p.

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34

Pedroni, Marco. "Equivalence of the Drinfeld-Sokolov reduction to a bi-Hamiltonian reduction." Letters in Mathematical Physics 35, no. 4 (1995): 291–302. http://dx.doi.org/10.1007/bf00750836.

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35

Dresse, Alain, Jean M. L. Fisch, Philippe Gregoire, and Marc Henneaux. "Equivalence of the Hamiltonian and Lagrangian path integrals for gauge theories." Nuclear Physics B 354, no. 1 (1991): 191–217. http://dx.doi.org/10.1016/0550-3213(91)90182-w.

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36

Grosse-Knetter, Carsten. "Equivalence of Hamiltonian and Lagrangian path integral quantization: Effective gauge theories." Physical Review D 49, no. 4 (1994): 1988–95. http://dx.doi.org/10.1103/physrevd.49.1988.

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37

Becker, W. "On the equivalence of the r·E and the p·A interaction hamiltonian." Optics Communications 56, no. 2 (1985): 107–11. http://dx.doi.org/10.1016/0030-4018(85)90211-1.

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38

Bahr, Benjamin, and Klaus Liegener. "Towards exploring features of Hamiltonian renormalisation relevant for quantum gravity." Classical and Quantum Gravity 39, no. 7 (2022): 075010. http://dx.doi.org/10.1088/1361-6382/ac5050.

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Abstract We consider the Hamiltonian renormalisation group (RG) flow of discretised one-dimensional physical theories. In particular, we investigate the influence the choice of different embedding maps has on the RG flow and the resulting continuum limit, and show in which sense they are, and in which sense they are not equivalent as physical theories. We are furthermore elucidating on the interplay of the RG flow and the algebras which operators satisfy, both on the discrete and the continuum. Further, we propose preferred renormalisation prescriptions for operator algebras guaranteeing to ar

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39

CASTAGNINO, M., M. L. LEVINAS, and N. UMÉREZ. "GRAVITATIONAL AND MATTER ENERGY–MOMENTUM DENSITIES AND EQUIVALENCE PRINCIPLE IN NON-RIEMANNIAN GEOMETRIES." International Journal of Modern Physics A 14, no. 30 (1999): 4721–34. http://dx.doi.org/10.1142/s0217751x99002219.

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We introduce an energy–momentum density vector which is independent of the affine structure of the manifold. Conservation of this quantity is linked to observers. Integrating over timelike surfaces, we define the Hamiltonian and momentum of the system which coincide with the corresponding standard ADM definitions when taking adequate asymptotical conditions. We define an Equivalence Principle for manifolds with torsion as a possible extension of the Equivalence Principle of General Relativity to non-Riemannian geometries.

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40

Muslih, S. I. "The equivalence between the Hamiltonian and Lagrangian formulations for the parametrization-invariant theories." International Journal of Mathematics and Mathematical Sciences 30, no. 1 (2002): 9–14. http://dx.doi.org/10.1155/s016117120201253x.

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The link between the treatment of singular Lagrangians as field systems and the canonical Hamiltonian approach is studied. It is shown that the singular Lagrangians as field systems are always in exact agreement with the canonical approach for the parametrization invariant theories.

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41

Golasiński, Marek. "On equivariant disconnected rational homotopy theory." gmj 17, no. 2 (2010): 229–40. http://dx.doi.org/10.1515/gmj.2010.008.

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Abstract An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G, let X be a G-simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪(G) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ X with the properties required by nonequivariant minimal algebras.

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42

Vedyushkina, V. V., and A. T. Fomenko. "Force Evolutionary Billiards and Billiard Equivalence of the Euler and Lagrange Cases." Doklady Mathematics 103, no. 1 (2021): 1–4. http://dx.doi.org/10.1134/s1064562421010154.

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Abstract A class of force evolutionary billiards is discovered that realizes important integrable Hamiltonian systems on all regular isoenergy 3-surfaces simultaneously, i.e., on the phase 4-space. It is proved that the well-known Euler and Lagrange integrable systems are billiard equivalent, although the degrees of their integrals are different (two and one).

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43

Abarbanel, Henry D. I., Paul J. Rozdeba, and Sasha Shirman. "Machine Learning: Deepest Learning as Statistical Data Assimilation Problems." Neural Computation 30, no. 8 (2018): 2025–55. http://dx.doi.org/10.1162/neco_a_01094.

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We formulate an equivalence between machine learning and the formulation of statistical data assimilation as used widely in physical and biological sciences. The correspondence is that layer number in a feedforward artificial network setting is the analog of time in the data assimilation setting. This connection has been noted in the machine learning literature. We add a perspective that expands on how methods from statistical physics and aspects of Lagrangian and Hamiltonian dynamics play a role in how networks can be trained and designed. Within the discussion of this equivalence, we show th

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44

HUQ, M., P. I. OBIAKOR, and S. SINGH. "POINT PARTICLE WITH EXTRINSIC CURVATURE." International Journal of Modern Physics A 05, no. 22 (1990): 4301–10. http://dx.doi.org/10.1142/s0217751x90001793.

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We have considered point particle action with extrinsic curvature having a geometric interpretation. It is shown that the Hamiltonian formalism possesses more gauge symmetries than the Lagrangian one. Equivalence of the BRST method in both formalisms is also exhibited.

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45

CONSTANTINESCU, RADU, and CARMEN IONESCU. "THE EQUIVALENCE BETWEEN THE LAGRANGIAN AND THE HAMILTONIAN FORMALISMS FOR THE EXTENDED BRST SYMMETRY." International Journal of Modern Physics A 21, no. 07 (2006): 1567–75. http://dx.doi.org/10.1142/s0217751x06023949.

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The analysis of the equivalence between the Hamiltonian and Lagrangian formalisms, for a sp(2) BRST theory, is achieved. The proof of this equivalence, apart from its intrinsic importance, allows the explanation of some results which seem artificially implanted in the theory: the structure of the extended spaces, and the form of the master equation. As a new image on the BRST operator, this paper suggests that its action can be split into a canonical part and a noncanonical part.

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46

Chen, Rong-Chao, and Xin Wu. "A Note on the Equivalence of Post-Newtonian Lagrangian and Hamiltonian Formulations." Communications in Theoretical Physics 65, no. 3 (2016): 321–28. http://dx.doi.org/10.1088/0253-6102/65/3/321.

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47

Huveneers, François, and Elias Theil. "Equivalence of Ensembles, Condensation and Glassy Dynamics in the Bose–Hubbard Hamiltonian." Journal of Statistical Physics 177, no. 5 (2019): 917–35. http://dx.doi.org/10.1007/s10955-019-02396-z.

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48

BAYRAKDAR, Tuna, and Abdullah Aziz ERGİN. "Equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds." TURKISH JOURNAL OF MATHEMATICS 42, no. 5 (2018): 2452–65. http://dx.doi.org/10.3906/mat-1708-33.

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49

Korovina, N. V. "Orbital equivalence of integrable Hamiltonian systems in neighborhoods of saddle-center leaves." Doklady Mathematics 73, no. 3 (2006): 399–402. http://dx.doi.org/10.1134/s1064562406030239.

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50

De Jonghe, Frank. "Schwinger-Dyson BRST symmetry and the equivalence of Hamiltonian and Lagrangian quantisation." Physics Letters B 316, no. 4 (1993): 503–9. http://dx.doi.org/10.1016/0370-2693(93)91035-l.

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