Quantization Without the Witten Anomalies (original) (raw)
Quantisation without Witten Anomalies
It is argued that the gauge anomalies are only the artefacts of quantum field theory when certain subtleties are not taken into account. With the Berry's phase needed to satisfy certain boundary conditions of the generating path integral, the gauge anomalies associated with homotopically nontrivial gauge transformations are shown explicitly to be eliminated, without any extra quantum fields introduced. This is in contra-distinction to other quantisations of 'anomalous' gauge theory where extra, new fields are introduced to explicitly cancel the anomalies.
Some Remarks on the Quantization of Gauge Theories
Journal of Mathematical Physics, 1995
The methods of reduced phase space quantization and Dirac quantization are examined in a simple gauge theory. A condition for the possible equivalence of the two methods is discussed.
Quantization of gauge fields without the path-integral formalism
Physical Review D, 1976
A general treatment is given for the quantization of gauge fields which makes use of the standard field theory but avoids the path-integral formalism. For this purpose, an appropriate extension of the procedure used for the quantization of the electromagnetic field with an indefinite metric is carried out by introducing nonphysical self-commuting fields. The treatment is applied to the Yang-Mills field, Einstein's gravitational field, and the Higgs model as examples of massless and massive gauge fields. Then, the gauge-compensating terms for an arbitrary gauge field are derived, and shown to be identical to those obtained by means of the path-integral formalism.
Quantization of field theories in the presence of boundaries
1996
This paper reviews the progress made over the last five years in studying boundary conditions and semiclassical properties of quantum fields about 4-realdimensional Riemannian backgrounds. For massless spin-1 2 fields one has a choice of spectral or supersymmetric boundary conditions, and the corresponding conformal anomalies have been evaluated by using zeta-function regularization. For Euclidean Maxwell theory in vacuum, the mode-by-mode analysis of BRST-covariant Faddeev-Popov amplitudes has been performed for relativistic and non-relativistic gauge conditions. For massless spin-3 2 fields, the contribution of physical degrees of freedom to one-loop amplitudes, and the 2-spinor analysis of Dirac and Rarita-Schwinger potentials, have been obtained. In linearized gravity, gauge modes and ghost modes in the de Donder gauge have been studied in detail. This program may lead to a deeper understanding of different quantization techniques for gauge fields and gravitation, to a new vision of gauge invariance, and to new points of view in twistor theory.
Second quantisation and the path integral of chiral gauge theories
Physics Letters B, 1989
The second quantisation of chiral gauge theories is reexamined and the path integral is derived in the holomorphic representation. It is shown that the effective action of the path integral contains an extra term preserving the gauge invariance, that is, the generating functional is free of anomaly. Various implications of the result are also discussed.
A modest redirection of quantum field theory solves all current problems
ArXiv, 2023
Standard quantization using, for example, path integration of field theory models, includes paths of momentum and field reach infinity in the Hamiltonian density, while the Hamiltonian itself remains finite. That fact causes considerable difficulties. In this paper, we represent π(x) by k(x)/ϕ(x). To insure proper values for π(x) it is necessary to restrict 0 < |ϕ(x)| < ∞ as well as 0 ≤ |k(x)| < ∞. Indeed that leads to Hamiltonian densities in which ϕ(x) p , where p can be even integers between 4 and ∞. This leads to a completely satisfactory quantization of field theories using situations that involve scaled behavior leading to an unexpected,h 2 /φ(x) 2 which arises only in the quantum aspects. Indeed, it is fair to claim that this symbol change leads to valid field theory quantizations.
Quantization and gauge invariance
1999
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the Heisenberg algebra over curved manifolds of non trivial topology involve topology classes of flat U(1) bundles. On the other hand, through some examples, the recently proposed physical projector approach to the quantisation of general gauge invariant systems is shown to avoid the necessity of any gauge fixing - hence also avoiding the possibility of Gribov problems which usually ensue any gauge fixing procedure - and is also capable to provide the adequate description of the physical content of gauge invariant systems. Comment: 12 pages, no figures, plain LaTeX file. Contribution to the First International Workshop on Contemporary Problems in Mathematical Physics, October 31st - November 5th, 1999, Cotonou (Republic of Benin)
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.