HAMILTONIAN BRST QUANTIZATION OF (1 + 1)-DIMENSIONAL MASSIVE VECTOR FIELDS

1996 ◽  
Vol 11 (18) ◽  
pp. 1509-1522 ◽  
Author(s):  
HIROHUMI SAWAYANAGI
Keyword(s):  
Vector Field ◽  
Laplace Transform ◽  
Vector Fields ◽  
Brst Quantization ◽  
Mass Term ◽  
Massive Vector ◽  
The Laplace Transform

The Lagrangian of a (1 + 1)-dimensional massive vector field is quantized. Since it gives the system with second-class constraints, following Batalin and Fradkin, we introduce additional fields. Although the Stueckelberg field is usually introduced, we can use a pseudoscalar field instead. The duality between them is discussed. We show that the Stueckelberg mass term is equivalent to the Laplace transform of the Lagrangian of the gauged Wess-Zumino-Witten model.

scholarly journals GENERALIZED BRST QUANTIZATION AND MASSIVE VECTOR FIELDS

1998 ◽  
Vol 13 (18) ◽  
pp. 3101-3120 ◽  
Author(s):  
ROBERT MARNELIUS ◽  
IKUO S. SOGAMI
Keyword(s):  
Vector Fields ◽  
Brst Quantization ◽  
Inner Product ◽  
Effective Theory ◽  
Product Spaces ◽  
Massive Vector ◽  
Yang Mills ◽  
Inner Product Spaces ◽  
Interaction Terms ◽  
Brst Charge

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.

HAMILTONIAN BRST QUANTIZATION OF AN ABELIAN MASSIVE VECTOR FIELD WITH AN ANTISYMMETRIC TENSOR FIELD

1995 ◽  
Vol 10 (10) ◽  
pp. 813-822 ◽  
Author(s):  
HIROHUMI SAWAYANAGI
Keyword(s):  
Vector Field ◽  
Tensor Field ◽  
Brst Quantization ◽  
Antisymmetric Tensor ◽  
Massive Vector ◽  
Fixed Action ◽  
Antisymmetric Tensor Field ◽  
Covariant Gauge ◽  
New Variables

The Lagrangian of an Abelian massive vector field gives a system with second class constraints. We apply the Batalin–Fradkin formalism, which converts second class constraints to first class ones through the introduction of new variables. As a new variable, instead of the Stueckelberg field, we introduce an antisymmetric tensor field. A covariant gauge-fixed action is presented. The unitarity and the duality are also discussed.

scholarly journals REDUCED PHASE SPACE QUANTIZATION OF MASSIVE VECTOR THEORY

1999 ◽  
Vol 14 (14) ◽  
pp. 2285-2308 ◽  
Author(s):  
H.-P. PAVEL ◽  
V. N. PERVUSHIN
Keyword(s):  
Vector Field ◽  
Phase Space ◽  
Vector Fields ◽  
Massless Limit ◽  
Massive Vector ◽  
Lorentz Covariance ◽  
Poincaré Algebra ◽  
Local Vector ◽  
Vector Theory ◽  
Fermion Current

We quantize massive vector theory in such a way that it has a well-defined massless limit. In contrast to the approach by Stückelberg where ghost fields are introduced to maintain manifest Lorentz covariance, we use reduced phase space quantization with nonlocal dynamical variables which in the massless limit smoothly turn into the photons, and check explicitly that the Poincaré algebra is fulfilled. In contrast to conventional covariant quantization our approach leads to a propagator which has no singularity in the massless limit and is well behaved for large momenta. For massive QED, where the vector field is coupled to a conserved fermion current, the quantum theory of the nonlocal vector fields is shown to be equivalent to that of the standard local vector fields. An inequivalent theory, however, is obtained when the reduced nonlocal massive vector field is coupled to a nonconserved classical current.

scholarly journals PATH INTEGRAL QUANTIZATION FOR MASSIVE VECTOR BOSONS

2010 ◽  
Vol 25 (18n19) ◽  
pp. 3603-3619 ◽  
Author(s):  
D. DJUKANOVIC ◽  
J. GEGELIA ◽  
S. SCHERER
Keyword(s):  
Vector Fields ◽  
Consistency Condition ◽  
Canonical Quantization ◽  
Mass Term ◽  
Effective Field ◽  
Coupling Constants ◽  
Massive Vector ◽  
Yang Mills ◽  
Interaction Terms ◽  
Vector Bosons

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.

scholarly journals Inflation driven by massive vector fields with derivative self-interactions

2019 ◽  
Vol 28 (04) ◽  
pp. 1950064 ◽  
Author(s):  
A. Oliveros ◽  
Marcos A. Jaraba
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Kinetic Term ◽  
Model Parameters ◽  
Tensor Model ◽  
De Sitter ◽  
Frw Universe ◽  
Derivative Coupling ◽  
Massive Vector ◽  
Slow Roll

Inspired by the Generalized Proca Theory, we study a vector–tensor model of inflation with massive vector fields and derivative self-interactions. The action under consideration contains a usual Maxwell-like kinetic term, a general potential term and a term with nonminimal derivative coupling between the vector field and gravity, via the dual Riemann tensor. In this theory, the last term contains a free parameter, [Formula: see text], which quantifies the nonminimal derivative coupling. In this scenario, taking into account a spatially flat Friedmann–Robertson–Walker (FRW) universe and a general vector field, we obtain the general expressions for the equation of motion and the total energy–momentum tensor. Choosing a Proca-type potential, a suitable inflationary regimen driven by massive vector fields is studied. In this model, the isotropy of expansion is guaranteed by considering a triplet of orthogonal vector fields. In order to obtain an inflationary solution with this model, the quasi de Sitter expansion was considered. In this case, the vector field behaves as a constant. Finally, slow-roll analysis is performed and slow-roll conditions are defined for this model, which, for suitable constraints of the model parameters, can give the required number of e-folds for sufficient inflation.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

scholarly journals Algebraic inversion of the Laplace transform

2005 ◽  
Vol 50 (1-2) ◽  
pp. 179-185 ◽  
Author(s):  
P.G. Massouros ◽  
G.M. Genin
Keyword(s):  
Laplace Transform ◽  
The Laplace Transform
Sign in / Sign up

Export Citation Format

Share Document