Treatment of a system with explicitly broken gauge symmetries (original) (raw)

Dirac on Gauges and Constraints

International Journal of Theoretical Physics, 2004

We examine the relevance of Dirac's view on the use of transformation theory and invariants in modern physics to current reflections on the meaning of physical symmetries, especially gauge symmetries.

Gauge transformations in Dirac theory of constrained systems

Journal of Mathematical Physics, 1990

According to Dirac's prescription the generator of gauge transformations for a constrained system endowed with primary and secondary first class constraints is constructed as a linear combination of all these (first class) constraints. Using the total Hamiltonian to generate the dynamics of the system it is shown that the time evolution of the coefficients of the secondary constraints in the generator of gauge transformations is not independent but is determined by the coefficients of the primary constraints. This result is applied to some physically interesting systems.

Quantization of gauge-invariant theories through the Dirac-bracket formalism

Physical Review D, 1981

A physical system possessing first-class constraints is quantized by using the Dirac-bracket formalism. The main features of this quantization procedure are analyzed. The model enables us to present a situation where gaugedependent Dirac brackets give origin to gauge-independent equations of motion,

Dirac Versus Reduced Phase Space Quantization for Systems Admitting No Gauge Conditions

International Journal of Modern Physics A, 1996

The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods for dealing with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of systems under consideration. It is found that the two quantization methods may give similar, or essentially different, physical results, and moreover a class of constrained systems, which can be quantized only by the Dirac method, is discussed. A possible interpretation of the gauge degrees of freedom is given.

Quantization of spontaneously broken gauge theories in the unitary gauge through the Dirac-bracket formalism

Il Nuovo Cimento A

We reconsider the quantization of the Higgs model in the unitary gauge using the Dirac-bracket quantization procedure. It is found that the structure of some of the equal-time commutators is quite abnormal. It is then shown in a very clear and systematic way that this anomalous structure is closely connected with the well-known quartically divergent contribution to the effective Higgs Lagrangian. This contribution has been shown to play an important role in the cancellation of nonrenormalizable divergences.

Quantization of constrained systems as Dirac first class versus second class: a toy model and its implications

2021

A toy model (suggested by Klauder) is analyzed from the perspective of First Class and Second Class Dirac constrained systems. The comparison is made by turning a First Class into a Second Class system with the introduction of suitable auxiliary conditions. The links between Dirac’s system of constraints, the Faddeev-Popov canonical functional integral method and the Maskawa-Nakajima procedure to reduced phase space are explicitly illustrated. The model reveals stark contrasts and physically distinguishable results between First and Second class routes. Physically relevant systems such as the relativistic point particle and electrodynamics are briefly recapped. Besides its pedagogical value, the article also advocates the route of rendering First Class into Second Class systems prior to quantization. Second Class systems lead to well-defined reduced phase space and physical observables; absence of inconsistencies in the closure of quantum constraint algebra; and consistent promotion...

Quantization of chiral antisymmetric tensor fields

2005

Chiral antisymmetric tensor fields can have chiral couplings to quarks and leptons. Their kinetic terms do not mix different representations of the Lorentz symmetry and a local mass term is forbidden by symmetry. The chiral couplings to the fermions are asymptotically free, opening interesting perspectives for a possible solution to the gauge hierarchy problem. We argue that the interacting theory for such fields can be consistently quantized, in contrast to the free theory which is plagued by unstable solutions. We suggest that at the scale where the chiral couplings grow large the electroweak symmetry is spontaneously broken and a mass term for the chiral tensors is generated non-perturbatively. Massive chiral tensors correspond to massive spin one particles that do not have problems of stability. We also propose an equivalent formulation in terms of gauge fields.

Solving Gauge Invariant Systems without Gauge Fixing: The Physical Projector in 0+1 Dimensional Theories

Annals of Physics, 1999

The projector onto gauge invariant physical states was recently constructed for arbitrary constrained systems. This approach, which does not require gauge fixing nor any additional degrees of freedom beyond the original ones-two characteristic features of all other available methods for quantising constrained dynamics-is put to work in the context of a general class of quantum mechanical gauge invariant systems. The cases of SO(2) and SO(3) gauge groups are considered specifically, and a comprehensive understanding of the corresponding physical spectra is achieved in a straightforward manner, using only standard methods of coherent states and group theory which are directly amenable to generalisation to other Lie algebras. Results extend by far the few examples available in the literature from much more subtle and delicate analyses implying gauge fixing and the characterization of modular space.

Generalized canonical quantization of antisymmetric tensor gauge theory

Physics Letters B, 1988

The gauge-fixing problem in the nonabelian antisymmetric tensor gauge theory is discussed by using the systematic hamiltonian BRST approach. The BRST symmetry of the quantum action is defined with an off-shell nilpotent BRST charge, which insures unitarity. The transition to the covariant lagrangian description, containing a trilinear ghost coupling, is obtained.

Gauge generators, Dirac's conjecture, and degrees of freedom for constrained systems

Annals of Physics, 1988

A necessary and sufficient condition for a function to be a generator of dynamical symmetry transformations in hamiltonian formalism is derived and presented in two forms, one of which involves an evolution operator connecting hamiltonian and lagrangian formalisms. As a particular case gauge transformations are studied. A careful distinction between gauge transformations of solutions of equations of motion and gauge transformations of points in phase space allows us to give a detinitive clarification of the so-called Dirac conjecture (that is to say: the "ad hoc" addition of all the secondary first class constraints to the hamiltonian). Finally, the gauge fixing procedure is studied in both hamiltonian and lagrangian formalisms, and it is proven, in a nontrivial way, that the true number of degrees of freedom is the same for both formalisms.