Bound states of the hamiltonian of a three-dimensional lattice Yang-Mills field with the gauge group U(1)

1980 ◽  
Vol 45 (2) ◽  
pp. 1027-1029
Author(s):  
F. G. Abdulla-Zade
Keyword(s):  
Gauge Group ◽  
Bound States ◽  
Three Dimensional ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Mills Field

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.

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 S-duality wall of SQCD from Toda braiding

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
B. Le Floch
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Domain Wall ◽  
Gauge Group ◽  
Domain Walls ◽  
Three Dimensional ◽  
Vertex Operators ◽  
Dual Operator ◽  
Yang Mills ◽  
Agt Correspondence

Abstract Exact field theory dualities can be implemented by duality domain walls such that passing any operator through the interface maps it to the dual operator. This paper describes the S-duality wall of four-dimensional $$ \mathcal{N} $$ N = 2 SU(N) SQCD with 2N hypermultiplets in terms of fields on the defect, namely three-dimensional $$ \mathcal{N} $$ N = 2 SQCD with gauge group U(N − 1) and 2N flavours, with a monopole superpotential. The theory is self-dual under a duality found by Benini, Benvenuti and Pasquetti, in the same way that T[SU(N)] (the S-duality wall of $$ \mathcal{N} $$ N = 4 super Yang-Mills) is self-mirror. The domain-wall theory can also be realized as a limit of a USp(2N − 2) gauge theory; it reduces to known results for N = 2. The theory is found through the AGT correspondence by determining the braiding kernel of two semi-degenerate vertex operators in Toda CFT.

scholarly journals The SUSY Yang–Mills plasma in a T-matrix approach

2015 ◽  
Vol 30 (24) ◽  
pp. 1550145 ◽  
Author(s):  
Gwendolyn Lacroix ◽  
Claude Semay ◽  
Fabien Buisseret
Keyword(s):  
Gauge Group ◽  
Bound States ◽  
Bound State ◽  
Lattice Data ◽  
Superstring Theory ◽  
Matrix Formulation ◽  
Yang Mills ◽  
Bound State Spectrum ◽  
T Matrix ◽  
Arbitrary Gauge

In this paper, the thermodynamic properties of [Formula: see text] supersymmetric Yang–Mills theory with an arbitrary gauge group are investigated. In the confined range, we show that identifying the bound state spectrum with a Hagedorn one coming from noncritical closed superstring theory leads to a prediction for the value of the deconfining temperature [Formula: see text] that agrees with recent lattice data. The deconfined phase is studied by resorting to a [Formula: see text]-matrix formulation of statistical mechanics in which the medium under study is seen as a gas of quasigluons and quasigluinos interacting nonperturbatively. Emphasis is put on the temperature range (1–5) [Formula: see text], where the interactions are expected to be strong enough to generate bound states. Binary bound states of gluons and gluinos are indeed found to be bound up to 1.4 [Formula: see text] for any gauge group. The equation of state is then computed numerically for [Formula: see text] and [Formula: see text], and discussed in the case of an arbitrary gauge group. It is found to be nearly independent of the gauge group and very close to that of nonsupersymmetric Yang–Mills when normalized to the Stefan–Boltzmann pressure and expressed as a function of [Formula: see text].

scholarly journals EFFECTIVE 't HOOFT–POLYAKOV MONOPOLES FROM PURE SU(3) GAUGE THEORY

2003 ◽  
Vol 18 (40) ◽  
pp. 2873-2886 ◽  
Author(s):  
VLADIMIR DZHUNUSHALIEV ◽  
DOUGLAS SINGLETON
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Degrees Of Freedom ◽  
Scalar Fields ◽  
Finite Energy ◽  
Gauge Fields ◽  
Yang Mills ◽  
Pure Gauge Theory ◽  
Energy Configurations ◽  
Mills Field

The well-known topological monopoles originally investigated by 't Hooft and Polyakov are known to arise in classical Yang–Mills–Higgs theory. With a pure gauge theory, it is known that the classical Yang–Mills field equation do not have such finite energy configurations. Here we argue that such configurations may arise in a semi-quantized Yang–Mills theory, where the original gauge group, SU(3), is reduced to a smaller gauge group, SU(2), and with some combination of the coset fields of the SU(3) to SU(2) reduction acting as effective scalar fields. The procedure is called semi-quantized since some of the original gauge fields are treated as quantum degrees of freedom, while others are postulated to be effectively described as classical degrees of freedom. Some speculation is offer on a possible connection between these monopole configurations and the confinement problem, and the nucleon spin puzzle.

scholarly journals Bound states of a system of two bosons with a spherically potential on a lattice

2021 ◽  
Vol 2070 (1) ◽  
pp. 012023
Author(s):  
J.I. Abdullaev ◽  
Sh.H. Ergashova ◽  
Y.S. Shotemirov
Keyword(s):  
Invariant Subspace ◽  
Schrödinger Operator ◽  
Bound States ◽  
Three Dimensional ◽  
Invariant Subspaces ◽  
Bound State ◽  
Schrodinger Operator ◽  
Dimensional Lattice

Abstract We consider a Hamiltonian of a system of two bosons on a three-dimensional lattice Z 3 with a spherically simmetric potential. The corresponding Schrödinger operator H(k) this system has four invariant subspaces L(123), L(1), L(2) and L(3). The Hamiltonian of this system has a unique bound state over each invariant subspace L(1), L(2) and L(3). The corresponding energy values of these bound states are calculated exactly.

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