Van Der Waerden Calculus With Commuting Spinor Variables and Applications to Supersymmetry

Constantinescu, Florin

doi:10.1142/s0217732305017251

Cited by 3 publications

(13 citation statements)

References 8 publications

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“…However, three sets of wave equations (17)(18)(19)(20)(21) can be diagonalised by the following transformations. The transformation for scalar wave equations (17)(18)(19) involves purely algebraic parameters:…”

Section: Solution Of the Equations Of Motionmentioning

confidence: 99%

“…The second order equations of motion that they satisfy (20)(21) imply that they also each have four on-shell complex components. Spinor wavefunctions that satisfy first order Dirac equations of motion have four complex components offshell and two complex components on-shell.…”

Section: Solution Of the Equations Of Motionmentioning

confidence: 99%

“…A Krein space approach for quantum mechanics in an indefinite space 18,19,20 can be used if the set of wavefunctions F can be divided into two sets of wavefunctions, F + and F − , which have positive definite norm F + |F + > 0 and negative definite norm F − |F − < 0. If projectors can be defined for the wavefunctions in each space such that P + F = F + and P − F = F − then a positive definite norm can be formed for the complete set of wavefunctions F |JF > 0 using the gram operator J = P + −P − .…”

Section: Removal Of Ghostsmentioning

confidence: 99%

“…If projectors can be defined for the wavefunctions in each space such that P + F = F + and P − F = F − then a positive definite norm can be formed for the complete set of wavefunctions F |JF > 0 using the gram operator J = P + −P − . In order to produce a positive definite scalar products in spaces of supersymmetric functions a similar construction has been found to be required 20,21,22 (in this paper we are concerned with the probability current density.) Another interpretation of this procedure is to define a Krein conjugate F K = (JF ) † and a rewrite the positive definite norm as F K |F .…”

Section: Removal Of Ghostsmentioning

confidence: 99%

“…Constantinescu has found that for general supersymmetric scalar products a Krein space approach is required for positivity 20,21,22 . A Krein space solution can also be applied to the Fock states used by Volkov and Pashnev 5 .…”

Section: Removal Of Ghostsmentioning

confidence: 99%

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The Superfield Quantisation of a Superparticle Action With an Extended Line Element

FitzGerald

2005

Int. J. Mod. Phys. A

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A massive superparticle action based on the generalised line element in N=1 global superspace is quantised canonically. A previous method of quantising this action, based on a Fock space analysis, showed that states existed in three supersymmetric multiplets, each of a different mass. The quantisation procedure presented uses the single first class constraint as an operator condition on a general N=1 superwavefunction. The constraint produces coupled equations of motion for the component wavefunctions. Transformations of the component wavefunctions are derived that decouple the equations of motion and partition the resulting wavefunctions into three separate supermultiplets. Unlike previous quantisations of superparticle actions in N=1 global superspace, the spinor wavefunctions satisfy the Dirac equation and the vector wavefunctions satisfy the Proca equation.The off-shell closure of the commutators of the supersymmetry transformations, that include mass parameters, are derived by the introduction of auxiliary wavefunctions.To avoid the ghosts arising in a previous Fock space quantisation an alternative conjugation is used in the definition of the current, based on a Krein space approach.

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