Particle spin dynamics as the grassmann variant of classical mechanics

Berezin, F. A.; Marinov, M. S.

doi:10.1016/0003-4916(77)90335-9

Cited by 729 publications

(532 citation statements)

References 32 publications

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“…Analogous results, with minor differences, were found in [8], while the general theory of quantization Fermi-Bose systems is explained in [6].…”

Section: Introductionsupporting

confidence: 70%

“…This was mainly raised by supersymmetries [5], but very soon the relevance of anticommuting variables in many other fields was realized, [6,7,8,9]. In particular it was shown that Grassmann variables are suitable tools for giving a classical description of spin [6,7,8] and internal degrees of freedom of elementary particles [10]. These dynamical theories described by Lagrangians involving ordinary c-numbers and anticommuting numbers (Grassmann variables) were called pseudoclassical theories and the general approach has been defined as pseudomechanics, due to the special nature of the variables occuring in the problem.…”

Section: Introductionmentioning

confidence: 99%

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Scalar and spinning particles in a plane-wave field

Barducci¹,

Giachetti²

2003

J. Phys. A: Math. Gen.

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We study the quantization problem of relativistic scalar and spinning particles interacting with a radiation electromagnetic field by using the path integral and the external source method. The spin degrees of freedom are described in terms of Grassmann variables and the Feynman kernel is obtained through functional integration on both Bose and Fermi variables. We provide rigourous proof that the Feynman amplitudes are only determined by the classical contribution and we explicitly evaluate the propagators.

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“…Analogous results, with minor differences, were found in [8], while the general theory of quantization Fermi-Bose systems is explained in [6].…”

Section: Introductionsupporting

confidence: 70%

Section: Introductionmentioning

confidence: 99%

Scalar and spinning particles in a plane-wave field

Barducci¹,

Giachetti²

2003

J. Phys. A: Math. Gen.

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“…It is important to stress that components of (14) can be interpreted as superfield components, so it is as if we were working with a particular superfield multiplet containing only these physical bosons and fermions. From (16) it is clear that δ ǫ acts as a supersymmetry generator, so that we can set…”

Section: Let Us Define the Generators Of Gr(dmentioning

confidence: 99%

A Journey Through Garden Algebras

Bellucci

Gates

Orazi

2006

Supersymmetric Mechanics – Vol. 1

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Summary. The main purpose of these lectures is to give a pedagogical overview on the possibility to classify and relate off-shell linear supermultiplets in the context of supersymmetric mechanics. A special emphasis is given to a recent graphical technique that turns out to be particularly effective for describing many aspects of supersymmetric mechanics in a direct and simplifying way. 2 S. Bellucci, S. J. Gates, Jr., E. Orazi

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“…The low-energy dynamics of spinning particles in a curved space with metric g µν (x) is described by the d = 1 supersymmetric σ-model [1]- [6] L = 1 2 g µν (x)ẋ µẋν + i 2 η ab ψ a Dψ b Dτ ,…”

mentioning

confidence: 99%