scholarly journals ZERO-BRANE MATRIX MECHANICS, MONOPOLES AND MEMBRANE APPROACH IN QCD

2000 ◽  
Vol 15 (04) ◽  
pp. 293-308 ◽  
Author(s):  
GREGORY GABADADZE ◽  
ZURAB KAKUSHADZE
Keyword(s):  
Quantum Mechanics ◽  
Gauge Symmetry ◽  
Moduli Space ◽  
Dimensional Space ◽  
Energy State ◽  
Matrix Mechanics ◽  
Large N ◽  
Dimensional Space Time ◽  
Generic Points ◽  
Matrix Quantum

We conjecture that a T-dual form of pure QCD describes dynamics of point-like monopoles. T-duality transforms the QCD Lagrangian into a matrix quantum mechanics of zero-branes which we identify with monopoles. At generic points of the monopole moduli space, the SU (N) gauge group is broken down to U (1)N-1 reproducing the key feature of 't Hooft's Abelian projection. There are certain points in the moduli space where monopole positions coincide, gauge symmetry is enhanced and gluons emerge as massless excitations. We show that there is a linearly rising potential between zero-branes. This indicates the presence of a stretched flux tube between monopoles. The lowest energy state is achieved when monopoles are sitting on top of each other and gauge symmetry is enhanced. In this case they behave as free massive particles and can be condensed. In fact, we find a constant eigenfunction of the corresponding Hamiltonian which describes condensation of monopoles. Using the monopole quantum mechanics, we argue that large-N QCD in this T-dual picture is a theory of a closed bosonic membrane propagating in five-dimensional space–time. QCD point-like monopoles can be regarded in this approach as constituents of the membrane.

scholarly journals Emergence of Time in Quantum Gravity: Is Time Necessarily Flowing?

KronoScope ◽  
2013 ◽  
Vol 13 (1) ◽  
pp. 67-84 ◽  
Author(s):  
Pierre Martinetti
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Proper Time ◽  
Dimensional Space ◽  
Thermal Time ◽  
List Type ◽  
State Dependent ◽  
Dimensional Space Time ◽  
Flow Of Time ◽  
Time In Quantum Mechanics

Abstract We discuss the emergence of time in quantum gravity and ask whether time is always “something that flows.” We first recall that this is indeed the case in both relativity and quantum mechanics, although in very different manners: time flows geometrically in relativity (i.e., as a flow of proper time in the four dimensional space-time), time flows abstractly in quantum mechanics (i.e., as a flow in the space of observables of the system). We then ask the same question in quantum gravity in the light of the thermal time hypothesis of Connes and Rovelli. The latter proposes to answer the question of time in quantum gravity (or at least one of its many aspects) by postulating that time is a state-dependent notion. This means that one is able to make a notion of time as an abstract flow—that we call the thermal time—emerge from the knowledge of both: the algebra of observables of the physical system under investigation; a state of thermal equilibrium of this system. Formally, the thermal time is similar to the abstract flow of time in quantum mechanics, but we show in various examples that it may have a concrete implementation either as a geometrical flow or as a geometrical flow combined with a non-geometric action. This indicates that in quantum gravity, time may well still be “something that flows” at some abstract algebraic level, but this does not necessarily imply that time is always and only “something that flows” at the geometric level.

scholarly journals Possible Unification of Quantum Mechanics and General Relativity Theory Based on the Three-Dimensional Quantized Spaces

2018 ◽  
Author(s):  
Jae-Kwang Hwang
Keyword(s):  
General Relativity ◽  
Wave Function ◽  
Quantum Mechanics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Energy Transition ◽  
Space Time ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Dimensional Space Time

Three-dimensional quantized space model is newly introduced. Quantum mechanics and relativity theory are explained in terms of the warped three-dimensional quantized spaces with the quantum time width (Dt=tq). The energy is newly defined as the 4-dimensional space-time volume of E = cDtDV in the present work. It is shown that the wave function of the quantum mechanics is closely related to the warped quantized space shape with the space time-volume. The quantum entanglement and quantum wave function collapse are explained additionally. The special relativity theory is separated into the energy transition associated with the space-time shape transition of the matter and the momentum transition associated with the space-time location transition. Then, the quantum mechanics and the general relativity theory are about the 4-dimensional space-time volume and the 4-dimensional space-time distance, respectively.

scholarly journals Non-Abelian Gauge Symmetry in the Causal Epstein–Glaser Approach

1997 ◽  
Vol 12 (24) ◽  
pp. 4461-4476 ◽  
Author(s):  
Tobias Hurth
Keyword(s):  
Perturbation Theory ◽  
Gauge Symmetry ◽  
Gauge Invariance ◽  
Fock Space ◽  
Dimensional Space ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Tree Graphs ◽  
Adiabatic Switching ◽  
Dimensional Space Time

Non-Abelian gauge symmetry in (3 + 1)-dimensional space–time is analyzed in the causal Epstein–Glaser framework. In this formalism, the technical details concerning the well-known UV and IR problem in quantum field theory are separated and reduced to well-defined problems, namely the causal splitting and the adiabatic switching of operator-valued distributions. Non-Abelian gauge invariance in perturbation theory is completely discussed in the well-defined Fock space of free asymptotic fields. The LSZ formalism is not used in this construction. The linear operator condition of asymptotic gauge invariance is sufficient for the unitarity of the S matrix in the physical subspace and the usual Slavnov–Taylor identities. We explicitly derive the most general specific coupling compatible with this condition. By analyzing only tree graphs in the second order of perturbation theory we show that the well-known Yang–Mills couplings with anticommuting ghosts are the only ones which are compatible with asymptotic gauge invariance. The required generalizations for linear gauges are given.

scholarly journals FIELD THEORETIC REALIZATIONS FOR CUBIC SUPERSYMMETRY

2004 ◽  
Vol 19 (32) ◽  
pp. 5585-5608 ◽  
Author(s):  
N. MOHAMMEDI ◽  
G. MOULTAKA ◽  
M. RAUSCH DE TRAUBENBERG
Keyword(s):  
Gauge Symmetry ◽  
Dimensional Space ◽  
A Priori ◽  
Space Time ◽  
Time Symmetry ◽  
Poincaré Algebra ◽  
Dimensional Space Time

We consider a four-dimensional space–time symmetry which is a nontrivial extension of the Poincaré algebra, different from supersymmetry and not contradicting a priori the well-known no-go theorems. We investigate some field theoretical aspects of this new symmetry and construct invariant actions for noninteracting fermion and noninteracting boson multiplets. In the case of the bosonic multiplet, where two-form fields appear naturally, we find that this symmetry is compatible with a local U(1) gauge symmetry, only when the latter is gauge fixed by a 't Hooft–Feynman term.

scholarly journals D-Brane Configurations and Nicolai Map in Supersymmetric Yang–Mills Theory

1997 ◽  
Vol 12 (03) ◽  
pp. 183-193 ◽  
Author(s):  
I. I. Kogan ◽  
R. J. Szabo ◽  
G. W. Semenoff
Keyword(s):  
Quantum Mechanics ◽  
Phase Transitions ◽  
Matrix Model ◽  
Short Distance ◽  
Dimensional Theory ◽  
Yang Mills ◽  
Large N ◽  
The Matrix ◽  
M Theory ◽  
Matrix Quantum

We discuss some properties of a supersymmetric matrix model that is the dimensional reduction of supersymmetric Yang–Mills theory in 10 dimensions and which has been recently argued to represent the short-distance structure of M-theory in the infinite momentum frame. We describe a reduced version of the matrix quantum mechanics and derive the Nicolai map of the simplified supersymmetric matrix model. We use this to argue that there are no phase transitions in the large-N limit, and hence that S-duality is preserved in the full 11-dimensional theory.

THE CHERN–SIMONS TERM AND THE DYNAMICS OF THE CPn−1 MODEL IN THREE DIMENSIONS

1992 ◽  
Vol 07 (03) ◽  
pp. 619-630 ◽  
Author(s):  
E. ABDALLA ◽  
F. M. DE CARVALHO
Keyword(s):  
Phase Structure ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Time ◽  
Three Dimensions ◽  
Rich Phase ◽  
Large N ◽  
Dimensional Space Time ◽  
Chern Simons ◽  
Three Dimensional Space

We analyze the phase structure of the CPn−1 model in three-dimensional space–time coupled to fermions, paying special attention to the role played by the Chern–Simons term generated by the fermions. A rich phase structure arises from the large-n expansion.

scholarly journals NONCOMMUTATIVE INSTANTONS AND THE INFORMATION METRIC

2002 ◽  
Vol 17 (06) ◽  
pp. 341-353 ◽  
Author(s):  
SHAHROKH PARVIZI
Keyword(s):  
Moduli Space ◽  
Dimensional Space ◽  
Space Time ◽  
First Order ◽  
Dimensional Space Time ◽  
Information Metric ◽  
Definition Of ◽  
Definition Of Information ◽  
Noncommutative Instantons

By using the so-called Information Metric on the moduli space of an anti-self-dual (ASD) Instanton in a self-dual (SD) noncommutative background, we investigate the geometry of moduli space. The metric is evaluated perturbatively in noncommutativity parameter and we show that by putting a cutoff in the location of instanton in the definition of Information Metric we can recover the five-dimensional space–time in the presence of a B-field. This result shows that the noncommutative YM-Instanton Moduli corresponds to D-Instanton Moduli in the gravity side where the radial and transverse location of D-Instanton correspond to YM-Instanton size and location, respectively. The match is shown in the first order of noncommutativity parameter.

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