Canonical quantization of lattice Higgs-Yang-Mills fields: Krein essential selfadjointness of the Hamiltonian

2016 ◽  
Vol 57 (6) ◽  
pp. 062301
Author(s):  
John L. Challifour ◽  
Edward J. Timko
Keyword(s):  
Canonical Quantization ◽  
Yang Mills ◽  
Essential Selfadjointness

Canonical quantization of the Yang-Mills Lagrangian with higher derivatives

1985 ◽  
Vol 28 (7) ◽  
pp. 554-556 ◽  
Author(s):  
D. M. Gitman ◽  
S. L. Lyakhovich ◽  
I. V. Tyutin
Keyword(s):  
Canonical Quantization ◽  
Yang Mills ◽  
Higher Derivatives

scholarly journals Structure of gauge theories

2021 ◽  
Vol 136 (3) ◽  
Author(s):  
Víctor Aldaya
Keyword(s):  
Canonical Quantization ◽  
Experimental Parameter ◽  
Diffeomorphism Groups ◽  
Gauge Groups ◽  
Yang Mills ◽  
Vector Potentials ◽  
Generalized Symmetry ◽  
Weinberg Angle ◽  
Stueckelberg Formalism ◽  
Fundamental Physical

AbstractElementary interactions are formulated according to the principle of minimal interaction although paying special attention to symmetries. In fact, we aim at rewriting any field theory on the framework of Lie groups, so that, any basic and fundamental physical theory can be quantized on the grounds of a group approach to quantization. In this way, connection theory, although here presented in detail, can be replaced by “jet-gauge groups” and “jet-diffeomorphism groups.” In other words, objects like vector potentials or vierbeins can be given the character of group parameters in extended gauge groups or diffeomorphism groups. As a natural consequence of vector potentials in electroweak interactions being group variables, a typically experimental parameter like the Weinberg angle $$\vartheta _W$$ ϑ W is algebraically fixed. But more general remarkable examples of success of the present framework could be the possibility of properly quantizing massive Yang–Mills theories, on the basis of a generalized Non-Abelian Stueckelberg formalism where gauge symmetry is preserved, in contrast to the canonical quantization approach, which only provides either renormalizability or unitarity, but not both. It proves also remarkable the actual fixing of the Einstein Lagrangian in the vacuum by generalized symmetry requirements, in contrast to the standard gauge (diffeomorphism) symmetry, which only fixes the arguments of the possible Lagrangians.

On the canonical quantization of Yang-Mills theories

1983 ◽  
Vol 219 (1) ◽  
pp. 125-142 ◽  
Author(s):  
John L. Friedman ◽  
Nicholas J. Papastamatiou
Keyword(s):  
Canonical Quantization ◽  
Yang Mills

scholarly journals COHERENT STATES AND THE QUANTIZATION OF (1+1)-DIMENSIONAL YANG–MILLS THEORY

2001 ◽  
Vol 13 (10) ◽  
pp. 1281-1305 ◽  
Author(s):  
BRIAN C. HALL
Keyword(s):  
Phase Space ◽  
Gauge Symmetry ◽  
Coherent States ◽  
Complex Structure ◽  
Canonical Quantization ◽  
Point Of View ◽  
Joint Work ◽  
Bargmann Transform ◽  
Yang Mills ◽  
New Family

This paper discusses the canonical quantization of (1+1)-dimensional Yang–Mills theory on a spacetime cylinder from the point of view of coherent states, or equivalently, the Segal–Bargmann transform. Before gauge symmetry is imposed, the coherent states are simply ordinary coherent states labeled by points in an infinite-dimensional linear phase space. Gauge symmetry is imposed by projecting the original coherent states onto the gauge-invariant subspace, using a suitable regularization procedure. We obtain in this way a new family of "reduced" coherent states labeled by points in the reduced phase space, which in this case is simply the cotangent bundle of the structure group K. The main result explained here, obtained originally in a joint work of the author with B. Driver, is this: The reduced coherent states are precisely those associated to the generalized Segal–Bargmann transform for K, as introduced by the author from a different point of view. This result agrees with that of K. Wren, who uses a different method of implementing the gauge symmetry. The coherent states also provide a rigorous way of making sense out of the quantum Hamiltonian for the unreduced system. Various related issues are discussed, including the complex structure on the reduced phase space and the question of whether quantization commutes with reduction.

scholarly journals SL(2, R) YANG-MILLS THEORY ON A CIRCLE

1994 ◽  
Vol 09 (35) ◽  
pp. 3245-3253 ◽  
Author(s):  
INGEMAR BENGTSSON ◽  
JOAKIM HALLIN
Keyword(s):  
Group Theory ◽  
Fixed Points ◽  
Configuration Space ◽  
Network Topology ◽  
Canonical Quantization ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Hyperbolic Fixed Points ◽  
Compact Case

The kinematic of SL (2, ℝ) Yang-Mills theory on a circle is considered, for reasons that are spelt out. The gauge transformations exhibit hyperbolic fixed points, and this results in a physical configuration space with a non-Hausdorff “network” topology. The ambiguity encountered in canonical quantization is then much more pronounced than in the compact case and cannot be resolved through the kind of appeal made to group theory in that case.

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.

CANONICAL QUANTIZATION OF YANG-MILLS ON A CIRCLE

1996 ◽  
Vol 08 (01) ◽  
pp. 85-102 ◽  
Author(s):  
J. DIMOCK
Keyword(s):  
Wilson Loop ◽  
Canonical Quantization ◽  
Irreducible Characters ◽  
Yang Mills ◽  
Temporal Gauge ◽  
First Case

The canonical quantization of YM on a circle in the temporal gauge is developed in two different mathematically rigorous formulations. In the first case the basic coordinates are the gauge potentials and we give a complete construction, but find no observables. In the second case the basic coordinates are the holonomy operators (Wilson loop operators) and here we also give a construction. A key ingredient is a proof that the irreducible characters of the holonomy operators are eigenvectors for the Hamiltonian.

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