scholarly journals Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics

1990 ◽  
Vol 131 (1) ◽  
pp. 51-107 ◽  
Author(s):  
Sergio Doplicher ◽  
John E. Roberts
Keyword(s):  
Gauge Group ◽  
Particle Physics ◽  
Field Algebra ◽  
Compact Gauge Group

Complexification of the Exceptional Jordan Algebra and Its Application to Particle Physics

2021 ◽  
Vol 61 ◽  
pp. 1-16
Author(s):  
Daniele Corradetti ◽  
Keyword(s):  
Standard Model ◽  
Gauge Group ◽  
Jordan Algebra ◽  
Particle Physics ◽  
Compact Form ◽  
Symmetric Extension ◽  
Grand Unified Theories ◽  
The Standard Model ◽  
Unified Theories ◽  
Standard Model Gauge Group

Recent papers contributed revitalizing the study of the exceptional Jordan algebra $\mathfrak{h}_{3}(\mathbb{O})$ in its relations with the true Standard Model gauge group $\mathrm{G}_{SM}$. The absence of complex representations of $\mathrm{F}_{4}$ does not allow $\Aut\left(\mathfrak{h}_{3}(\mathbb{O})\right)$ to be a candidate for any Grand Unified Theories, but the automorphisms of the complexification of this algebra, i.e., $\mathfrak{h}_{3}^{\mathbb{C}}(\mathbb{O})$, are isomorphic to the compact form of $\mathrm{E}_{6}$ and similar constructions lead to the gauge group of the minimal left-right symmetric extension of the Standard Model.

Self-duality in four-dimensional Riemannian geometry

1978 ◽  
Vol 362 (1711) ◽  
pp. 425-461 ◽  
Keyword(s):  
Gauge Group ◽  
Riemannian Geometry ◽  
Complex Analysis ◽  
Three Dimensional ◽  
The Self ◽  
Full Detail ◽  
Yang Mills ◽  
Self Duality ◽  
Compact Gauge Group

We present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis. In particular we apply this to the self-dual Yang-Mills equations in Euclidean 4-space and compute the number of moduli for any compact gauge group. Results previously announced are treated with full detail and extended in a number of directions.

On the gauge orbit types for theories with classical compact gauge group

2010 ◽  
Vol 66 (3) ◽  
pp. 331-353 ◽  
Author(s):  
A. Hertsch ◽  
G. Rudolph ◽  
M. Schmidt
Keyword(s):  
Gauge Group ◽  
Orbit Types ◽  
Compact Gauge Group

YANG-MILLS FIELD QUANTIZATION WITH NON-COMPACT GAUGE GROUP

1992 ◽  
Vol 07 (29) ◽  
pp. 2747-2752 ◽  
Author(s):  
A. E. MARGOLIN ◽  
V. I. STRAZHEV
Keyword(s):  
State Space ◽  
Gauge Group ◽  
Physical State ◽  
Indefinite Metric ◽  
Yang Mills ◽  
S Matrix ◽  
Field Quantization ◽  
Compact Gauge Group ◽  
Mills Field

Yang-Mills field quantization in BRST-formalism with non-compact semi-simple gauge group is performed. The S-matrix unitarity in the physical state space, having indefinite metric is determined.

scholarly journals EXACT SOLUTION OF THE SCHWINGER MODEL WITH COMPACT U(1)

2001 ◽  
Vol 16 (03) ◽  
pp. 121-133
Author(s):  
ROMÁN LINARES ◽  
LUIS F. URRUTIA ◽  
J. DAVID VERGARA
Keyword(s):  
Exact Solution ◽  
Harmonic Oscillator ◽  
Gauge Group ◽  
Electric Charge ◽  
Axial Current ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Zero Modes ◽  
Compact Gauge Group ◽  
Θ Vacuum

The exact solution of the Schwinger model with compact gauge group U(1) is presented. The compactification is imposed by demanding that the only surviving true electromagnetic degree of freedom c has angular character. Not surprisingly, this topological condition defines a version of the Schwinger model which is different from the standard one, where c takes values on the line. The main consequences are: The spectra of the zero modes is not degenerated and does not correspond to the equally spaced harmonic oscillator, both the electric charge and a modified gauge-invariant chiral charge are conserved (nevertheless, the axial-current anomaly is still present) and, finally, there is no need to introduce a θ-vacuum. A comparison with the results of the standard Schwinger model is pointed out along the text.

scholarly journals MASSLESS PARTICLES, ELECTROMAGNETISM, AND RIEFFEL INDUCTION

1995 ◽  
Vol 07 (06) ◽  
pp. 923-958 ◽  
Author(s):  
N.P. LANDSMAN ◽  
U.A. WIEDEMANN
Keyword(s):  
Gauge Group ◽  
Symplectic Reduction ◽  
Abelian Gauge ◽  
Field Algebra ◽  
Covariant Representations ◽  
Sesquilinear Form ◽  
Induction Technique ◽  
Irreducible Unitary Representations ◽  
Algebra Theory ◽  
Relativistic Particles

The connection between space-time covariant representations (obtained by inducing from the Lorentz group) and irreducible unitary representations (induced from Wigner’s little group) of the Poincaré group is re-examined in the massless case. In the situation relevant to physics, it is found that these are related by Marsden-Weinstein reduction with respect to a gauge group. An analogous phenomenon is observed for classical massless relativistic particles. This symplectic reduction procedure can be (‘second’) quantized using a generalization of the Rieffel induction technique in operator algebra theory, which is carried through in detail for electromagnetism. Starting from the so-called Fermi representation of the field algebra generated by the free abelian gauge field, we construct a new (‘rigged’) sesquilinear form on the representation space, which is positive semi-definite, and given in terms of a Gaussian weak distribution (promeasure) on the gauge group (taken to be a Hilbert Lie group). This eventually constructs the algebra of observables of quantum electromagnetism (directly in its vacuum representation) as a representation of the so-called algebra of weak observables induced by the trivial representation of the gauge group.

scholarly journals Lepton flavor violating decays of B and K mesons in models with extended gauge group

2018 ◽  
Vol 33 (14n15) ◽  
pp. 1850087 ◽  
Author(s):  
Fayyazuddin ◽  
Muhammad Jamil Aslam ◽  
Cai-Dian Lu
Keyword(s):  
Gauge Group ◽  
Particle Physics ◽  
Neutral Current ◽  
Representation Formula ◽  
Decay Modes ◽  
Lepton Flavor ◽  
Flavor Changing ◽  
Effective Lagrangian ◽  
Flavor Changing Neutral Current ◽  
Promising Area

Lepton flavor violating (LFV) decays are forbidden in the Standard Model (SM) and to explore them one has to go beyond it. The flavor changing neutral current induced lepton flavor conserving and LFV decays of [Formula: see text] and [Formula: see text] mesons is discussed in the gauge group [Formula: see text]. The lepto-quark [Formula: see text] corresponding to gauge group [Formula: see text] allows the quark–lepton transitions and hence giving a framework to construct the effective Lagrangian for the LFV decays. The mass of lepto-quark [Formula: see text] provides a scale at which the gauge group [Formula: see text] is broken to the SM gauge group. Using the most stringent experimental limit [Formula: see text], the upper bound on the effective coupling constant [Formula: see text] is obtained for certain pairing of lepton and quark generations in the representation [Formula: see text] of the group [Formula: see text]. Later, the effective Lagrangian for the LFV meson decays for the gauge group [Formula: see text] is constructed. Using [Formula: see text], the bound on the ratio of effective couplings is obtained to be [Formula: see text]. A number of decay modes are discussed which provide a promising area to test this model in the current and future particle physics experiments.

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