Definite and indefinite inner products on superspace (Hilbert–Krein superspace)

Constantinescu, Florin

doi:10.1088/0305-4470/38/6/014

Cited by 19 publications

(57 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above formulas are very similar to the usual one in the supersymmetric literature [3,5,1] but not quite identical to them. The reason is our commutative convention which in particular modifies the sign in front ofσ (see relation (2.11 )).…”

Section: Commutative Van Der Waerden Calculussupporting

confidence: 80%

“…Note that these formulas are very similar (but not identical) to the coresponding formulas deduced under the anticommuting spinor convention (see [3,5,1]). Again, they are connected by a change of sign of the Pauli matrix σ.…”

Section: Commutative Van Der Waerden Calculussupporting

confidence: 58%

“…The overlap plays a major role for the massless vector field [1]. In the Hilbert space approach to follow the overlap will contain only factorizable vectors of zero length.…”

Section: Commutative Van Der Waerden Calculusmentioning

confidence: 99%

“…These expressions have to be compared with the corresponding expressions in the anticommuting case [1]:…”

Section: Commutative Van Der Waerden Calculusmentioning

confidence: 99%

See 3 more Smart Citations

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

Constantinescu

2005

Mod. Phys. Lett. A

Self Cite

View full text Add to dashboard Cite

Working with anticommuting Weyl (or Majorana) spinors in the frame of the van der Waerden calculus is standard in supersymmetry. The natural framework of rigorous supersymmetric quantum field theory makes use of operator-valued superdistributions defined on supersymmetric test functions. This makes necessary a van der Waerden calculus in which the Grassmann variables anticommute but the fermionic components are commutative instead of being anticommutative. We work out such a calculus in view of applications to the rigorous conceptual problems of supersymmetric quantum field theory.

show abstract

Section: Commutative Van Der Waerden Calculussupporting

confidence: 80%

Section: Commutative Van Der Waerden Calculussupporting

confidence: 58%

“…The overlap plays a major role for the massless vector field [1]. In the Hilbert space approach to follow the overlap will contain only factorizable vectors of zero length.…”

Section: Commutative Van Der Waerden Calculusmentioning

confidence: 99%

“…These expressions have to be compared with the corresponding expressions in the anticommuting case [1]:…”

Section: Commutative Van Der Waerden Calculusmentioning

confidence: 99%

See 2 more Smart Citations

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

Constantinescu

2005

Mod. Phys. Lett. A

Self Cite

View full text Add to dashboard Cite

show abstract

“…[10,27] where the solutions are superprojected in a sector of the physical states that is not chiral or antichiral.…”

Section: Tricmentioning

confidence: 99%

Non-compact Groups, Coherent States, Relativistic Wave Equations and the Harmonic Oscillator

Cirilo-Lombardo

2007

Found Phys

View full text Add to dashboard Cite

The physical meaning of the particularly simple non-degenerate supermetric, introduced in the previous part by the authors, is elucidated and the possible connection with processes of topological origin in high energy physics is analyzed and discussed. New possible mechanism of the localization of the fields in a particular sector of the supermanifold is proposed and the similarity and differences with a 5-dimensional warped model are shown. The relation with gauge theories of supergravity based in the OSP (1/4) group is explicitly given and the possible original action is presented. We also show that in this non-degenerate super-model the physic states, in contrast with the basic states, are observables and can be interpreted as tomographic projections or generalized representations of operators belonging to the metaplectic group M p (2) .The advantage of geometrical formulations based on non-degenerate super-manifolds over degenerate ones is pointed out and the description and the analysis of some interesting aspects of the simplest Riemannian superspaces are presented from the point of view of the possible vacuum solutions .

show abstract

A supersymmetric extension of quantum gauge theory

Grigore

Scharf

2003

Ann. Phys.

View full text Add to dashboard Cite

We consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. The constructions of the model follows closely the usual construction of gauge models in the Epstein-Glaser framework for perturbative field theory. Accordingly, all the arguments are completely of quantum nature without reference to a classical supersymmetric theory.As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.

show abstract

Definite and indefinite inner products on superspace (Hilbert–Krein superspace)

Abstract: We present natural (invariant) definite and indefinite scalar products on the N = 1 superspace which turns out to carry an inherent Hilbert-Krein structure. We are motivated by supersymmetry in physics but prefer a general mathematical framework.

Cited by 19 publications

References 6 publications

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

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

Non-compact Groups, Coherent States, Relativistic Wave Equations and the Harmonic Oscillator

A supersymmetric extension of quantum gauge theory

Contact Info

Product

Resources

About