Quantization of gauge theories

A path-integral procedure for quantizing gauge theories is proposed (on a heuristic level). The Hilbert space of physical states is constructed. Each physical state is represented by an infinite set of gauge equivalent configurations. All physical transition amplitudes are defined. In this approach, the “natural” value of parameter θ is zero.     

Quantization of chiral gauge theories in two-dimensions

It is shown that both abelian and non abelian chiral gauge theories in two dimensions can be made gauge invariant at the quantum level by adding a scalar field. In the bosonized form of the theory, the scalar field appears in a gauged Wess-Zumino action. The current algebra of the extended abelian theory is shown to be free of anomalous terms.     

Quantization of gauge theories with global anomalies

Global anomalies, which obstruct the quantization of certain gauge theories in the temporal gauge, get bypassed in canonical quantization.     

Quantization and unitary in antisymmetric tensor gauge theories

Following the procedure of Batalin and Vilkovisky we discuss the quantization of a non-abelian antisymmetric tensor gauge theory and describe the verification of one-loop unitarity for the quantized model, using the Ward identities and the procedure of 't Hooft and Veltman. The quantization of this system is similar to that of the Witten string field theory, requiring among other things the presence of three-ghost couplings.     

Quantization of gauge fields through fibre bundle multiconnectivity

A geometric model for the quantum nature of interaction fields is proposed. We utilize a trivial fibre bundle whose typical fibre has a multiconnectivity characterized by a discrete group Γ. By seeing Γ as a gauge group with global action on each fibre, we show that the corresponding field strength is non-zero only on the future part of the light cone whose vertex is at the interaction point. When the interaction is submitted to the symmetries of a Lie group G, we consider the gauge group G x Γ. The field strength of the gauge having this group includes a term expressing the quantization of the interaction field described by G. This geometric interpretation of quantization makes use of topological arguments similar to those applied to explain the Aharonov-Bohm effect. Two examples show how this interpretation applies to the cases of electromagnetic and gravitational fields.      

Quantization of gauge fields,graph polynomials and graph homology

We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n$n$ loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials.     

Quantization of non-abelian gauge theory. I. Gauge invariant Hamiltonian formulation

An essentially gauge invariant canonical Hamiltonian formulation is given for a non-Abelian Yang-Mills system coupled to a fermion field. The Hamiltonian contains only unconstrained dynamical variables, which in the quantum version satisfy canonical equal time commutation relations.     

Some results for SU(N) gauge-fields on the Hypertorus

We show how to prove and to understand the formula for the “Pontryagin” indexP for SU(N) gauge fields on the HypertorusT ⁴, seen as a four-dimensional euclidean box with twisted boundary conditions. These twists are defined as gauge invariant integers moduloN and labelled byN _μv (=?N _μv ). In terms of these we can write (ν∈#x2124;) $$P = \frac{1}{{16\pi ^2 }}\int {Tr(G_{\mu v} \tilde G_{\mu v} )d_4 x = v + \left( {\frac{{N - 1}}{N}} \right) \cdot \frac{{n_{\mu v} \tilde n_{\mu v} }}{4}} $$ . Furthermore we settle the last link in the proof of the existence of zero action solutions with all possible twists satisfying \(\frac{{n_{\mu v} \tilde n_{\mu v} }}{4} = \kappa (n) = 0(\bmod N)\) for arbitraryN.     

Quantization in the large

A model theory is constructed that exhibits quantization on a cosmic scale. A holistic rationale for the theory is discussed. The theory incorporates a fundamental length, of cosmic size, and preserves the weak, geometrical equivalence principle. The momentum operator is an integral, nonlocal, naturally contravariant operator, in contrast to the usual quantum case. In the limit of high quantum numbers the theory reduces to classical physics, giving rise to a world which is quantized both on the microscopic and cosmic scale, each of which passes over to the usual macroscopic, continuous, classical, world in the highn limit. The theory is applied to two experimental situations, absorption lines in high-z quasars and elliptical rings around normal galaxies, with suggestive but not definitive results.     

Quantization in the high-spin RPA

The problem of how to quantize the angular momentum of the self-consistent cranking model at high spin when small oscillations (RPA) about the steady rotation are included is reexamined, in view of a recent criticism by Reinhardt of an earlier treatment. This criticism is shown to be unfounded. On the other hand, it is shown that Reinhardt's quantization procedure leads to some serious problems, and the result that the vibrational frequencies differ in the rotating and lab frames is called into question.     

Stochastic quantisation of a gauge field in the spatial axial gauge

The stochastic quantisation method of Nelson can be applied to quantise an Abelian gauge field in the spatial axial gauge.     

VII. Difficulties in fixing the gauge in non-Abelian gauge theories

Some problems arising from the use of the Coulomb gauge in SU(2) Yang-Mills theory are discussed. It is shown that: i) the transversality condition does not fix the gauge uniquely (Gribov ambiguity); ii) there exist physical configurations that cannot be described by a continuous A_μ in the Coulomb gauge.