scholarly journals QUANTIZATION OF THE FREEDMAN–TOWNSEND MODEL OF MASSIVE VECTOR MESONS

1991 ◽  
Vol 06 (36) ◽  
pp. 3359-3363 ◽  
Author(s):  
M. LEBLANC ◽  
D. G. C. McKEON ◽  
A. REBHAN ◽  
T. N. SHERRY
Keyword(s):  
Vector Fields ◽  
Symmetric Tensor ◽  
Vector Mesons ◽  
Tensor Fields ◽  
Gauge Invariant ◽  
Massive Vector ◽  
Four Dimensions ◽  
Vector Gauge ◽  
Invariant Coupling ◽  
The Masses

We examine a model for massive vector mesons in four dimensions proposed by Freedman and Townsend, where the masses for non-Abelian vector gauge fields are generated without symmetry breaking through a gauge invariant coupling to anti-symmetric tensor fields. The model is quantized using the formalism of Batalin and Vilkovisky. While the Abelian version immediately gives a renormalizable model for massive vector fields, it is shown that in the non-Abelian case the addition of an extra gauge invariant term in the initial Lagrangian leads to an ultraviolet behavior consistent with power-counting renormalizability.

UNCONSTRAINED HIGHER SPINS IN FOUR DIMENSIONS

2011 ◽  
Vol 08 (03) ◽  
pp. 511-556 ◽  
Author(s):  
GIUSEPPE BANDELLONI
Keyword(s):  
Equations Of Motion ◽  
Symmetric Tensor ◽  
Tensor Fields ◽  
Geometrical Meaning ◽  
Four Dimensions ◽  
Spin Field ◽  
Angular Momenta ◽  
Higher Spin ◽  
Spin Fields ◽  
The Right

The relativistic symmetric tensor fields are, in four dimensions, the right candidates to describe Higher Spin Fields. Their highest spin content is isolated with the aid of covariant conditions, discussed within a group theory framework, in which auxiliary fields remove the lower intrinsic angular momenta sectors. These conditions are embedded within a Lagrangian Quantum Field theory which describes an Higher Spin Field interacting with a Classical background. The model is invariant under a (B.R.S.) symmetric unconstrained tensor extension of the reparametrization symmetry, which include the Fang–Fronsdal algebra in a well defined limit. However, the symmetry setting reveals that the compensator field, which restore the Fang–Fronsdal symmetry of the free equations of motion, is in the existing in the framework and has a relevant geometrical meaning. The Ward identities coming from this symmetry are discussed. Our constraints give the result that the space of the invariant observables is restricted to the ones constructed with the Highest Spin Field content. The quantum extension of the symmetry reveals that no new anomaly is present. The role of the compensator field in this result is fundamental.

Supersymmetric quantum field theory (QFT): Introduction

2021 ◽  
pp. 656-669
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Cosmological Constant ◽  
Particle Physics ◽  
Vector Fields ◽  
Hadron Collider ◽  
Large Mass ◽  
Momentum Tensor ◽  
Fine Tuning ◽  
Four Dimensions ◽  
New Feature ◽  
The Masses

Supersymmetry has been proposed, in particular as a principle to solve the so-called fine-tuning problem in particle physics by relating the masses of scalar particles (like Higgs fields) to those of fermions, which can be protected against ‘large’ mass renormalization by chiral symmetry. However, supersymmetry is, at best, an approximate symmetry broken at a scale beyond the reach of a large hadron collider (LHC), because the possible supersymmetric partners of known particles have not been discovered yet (2020) and thus, if they exist, must be much heavier. Exact supersymmetry would also have implied the vanishing of the vacuum energy and thus, of the cosmological constant. The discovery of dark energy has a natural interpretation as resulting from a very small cosmological constant. However, a naive model based on broken supersymmetry would still predict 60 orders of magnitude too large a value compared to 120 orders of magnitude otherwise. Gauging supersymmetry leads naturally to a unification with gravity, because the commutators of supersymmetry currents involve the energy momentum tensor. First, examples of supersymmetric theories involving scalar superfields, simple generalizations of supersymmetric quantum mechanics (QM) are described. The new feature of supersymmetry in higher dimensions is the combination of supersymmetry with spin, since fermions have spins. In four dimensions, theories with chiral scalar fields and vector fields are constructed.

scholarly journals Gauge invariant composite fields out of connections, with examples

2014 ◽  
Vol 11 (03) ◽  
pp. 1450016 ◽  
Author(s):  
C. Fournel ◽  
J. François ◽  
S. Lazzarini ◽  
T. Masson
Keyword(s):  
Field Theory ◽  
Particle Physics ◽  
Vector Fields ◽  
Gauge Field Theory ◽  
Gauge Invariant ◽  
Massive Vector ◽  
Valued Field ◽  
The Standard Model ◽  
Breaking Mechanism ◽  
New Situation

In this paper, we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group-valued field with a prescribed gauge transformation. As an illustration, we detail some examples. Two of them are based on known results: the first one provides a reinterpretation of the symmetry breaking mechanism of the electroweak part of the Standard Model of particle physics; the second one is an application to Einstein's theory of gravity described as a gauge theory in terms of Cartan connections. The last example depicts a new situation: starting with a gauge field theory on Atiyah Lie algebroids, the gauge invariant composite fields describe massive vector fields. Some mathematical and physical discussions illustrate and highlight the relevance and the generality of this approach.

scholarly journals RECTANGULAR MIXED FINITE ELEMENTS FOR ELASTICITY

2005 ◽  
Vol 15 (09) ◽  
pp. 1417-1429 ◽  
Author(s):  
DOUGLAS N. ARNOLD ◽  
GERARD AWANOU
Keyword(s):  
Finite Elements ◽  
Vector Fields ◽  
Mixed Finite Elements ◽  
Symmetric Tensor ◽  
Plane Elasticity ◽  
Discrete Version ◽  
Tensor Fields ◽  
Piecewise Polynomials ◽  
The Family ◽  
Differential Complex

We present a family of stable rectangular mixed finite elements for plane elasticity. Each member of the family consists of a space of piecewise polynomials discretizing the space of symmetric tensor fields in which the stress field is sought, and another to discretize the space of vector fields in which the displacement is sought. These may be viewed as analogues in the case of rectangular meshes of mixed finite elements recently proposed for triangular meshes. As for the triangular case the elements are closely related to a discrete version of the elasticity differential complex.

GAUGED SU(2)L×SU(2)R/SU(2)L+Rσ MODEL IN THE FRAMEWORK OF NONCOMMUTATIVE GEOMETRY

1994 ◽  
Vol 09 (31) ◽  
pp. 5531-5539 ◽  
Author(s):  
DAE SUNG HWANG ◽  
TAEHOON LEE
Keyword(s):  
Noncommutative Geometry ◽  
Vector Fields ◽  
Axial Vector ◽  
Scalar Fields ◽  
Gauge Fields ◽  
The Matrix ◽  
Vector Gauge ◽  
The Masses ◽  
Higgs Fields ◽  
Matrix Derivative

We study the gauged SU(2) L× SU(2) Rσ model in the SU(2|2) superalgebra formalism. The superconnection is taken to have one-form vector fields as its even part and zero-form scalar fields as its odd part. Incorporating the matrix derivative of noncommutative geometry proposed by Connes and Coquereaux et al., we naturally obtain the spontaneously symmetry broken SU(2) L× SU(2) Rσ model. The masses of the axial vector gauge fields and the Higgs fields are obtained.

The free field

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Gauge Invariance ◽  
Maxwell Equations ◽  
Degrees Of Freedom ◽  
Vector Fields ◽  
Initial Conditions ◽  
Free Field ◽  
Maxwell Theory ◽  
Gauge Invariant ◽  
Massive Vector ◽  
The One

This chapter studies the structure of Maxwell’s equations in a vacuum and the action from which they are derived, while emphasizing the consequences of their gauge invariance. Gauge invariance, on the one hand, allows one of the components of the magnetic potential to be chosen freely. Here, the chapter shows how the gauge-invariant version of the Maxwell equations in the vacuum can also be derived directly by extremizing. On the other hand, the chapter argues that gauge invariance imposes a constraint on the initial conditions such that in the end the general solution has only two ‘degrees of freedom’. Finally, the chapter develops the Hamiltonian formalisms in the Maxwell theory and compares them to the formalisms using non-gauge-invariant or massive vector fields.

Hamiltonian formulation of the Freedman–Townsend model of massive vector mesons

1991 ◽  
Vol 69 (5) ◽  
pp. 569-572 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Effective Action ◽  
Invariant Theory ◽  
Hamiltonian Formulation ◽  
Power Counting ◽  
Constrained Systems ◽  
Vector Mesons ◽  
Gauge Invariant ◽  
Massive Vector ◽  
Hamiltonian Theory

A gauge invariant theory of massive vector mesons, formulated by Freedman and Townsend, is quantized using the Hamiltonian theory for reducible constrained systems of Batalin, Fradkin, and Vilkovisky. The effective action is Lorentz covariant in the gauge in which we work. All propagators have an ultraviolet behaviour that is consistent with power-counting renormalizability. We take this formulation of the Freedman–Townsend model to be consistent with unitarity.

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