scholarly journals GENERALIZED BRST QUANTIZATION AND MASSIVE VECTOR FIELDS

1998 ◽  
Vol 13 (18) ◽  
pp. 3101-3120 ◽  
Author(s):  
ROBERT MARNELIUS ◽  
IKUO S. SOGAMI

A previously proposed generalized BRST quantization on inner product spaces for second class constraints is further developed through applications. This BRST method involves a conserved generalized BRST charge Q which is not nilpotent, Q2≠0, but which satisfies Q=δ+δ†, δ2=0, and by means of which physical states are obtained from the projection δ| ph >=δ†| ph >=0. A simple model is analyzed in detail from which some basic properties and necessary ingredients are extracted. The method is then applied to a massive vector field. An effective theory is derived which is close to that of the Stückelberg model. However, since the scalar field here is introduced in order to have inner product solutions, a massive Yang–Mills theory with polynomial interaction terms might be possible to cosntruct.

2010 ◽  
Vol 25 (18n19) ◽  
pp. 3603-3619 ◽  
Author(s):  
D. DJUKANOVIC ◽  
J. GEGELIA ◽  
S. SCHERER

A parity-conserving and Lorentz-invariant effective field theory of self-interacting massive vector fields is considered. For the interaction terms with dimensionless coupling constants the canonical quantization is performed. It is shown that the self-consistency condition of this system with the second-class constraints in combination with the perturbative renormalizability leads to an SU(2) Yang–Mills theory with an additional mass term.


2000 ◽  
Vol 15 (06) ◽  
pp. 833-867 ◽  
Author(s):  
ROBERT MARNELIUS ◽  
NICLAS SANDSTRÖM

There is an elaborated abstract form of BRST quantization on inner product spaces within the operator formalism which leads to BRST-invariant states of the form [Formula: see text] where ψ is a gauge fixing fermion, and where |ϕ> is a BRST-invariant state determined by simple Hermitian conditions. These state representations are closely related to the path integral formulation. Here we analyse the basics of this approach in detail. The freedom in the choice of ψ and |ϕ> as well as their properties under gauge transformations are explicitly determined for simple Abelian models. In all considered cases SL(2,R) is shown both to be a natural extended gauge symmetry and to be useful to determine |ph>. The results are also applied to non-Abelian models.


Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 765
Author(s):  
Lorena Popa ◽  
Lavinia Sida

The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta’s definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type Nădăban-Dzitac. Finally, some challenges are given.


1989 ◽  
Vol 144 (1) ◽  
pp. 81-86
Author(s):  
Charles R. Diminnie ◽  
Edward Z. Andalafte ◽  
Raymond W. Freese

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