scholarly journals Covariant origin of the U(1)3 model for Euclidean quantum gravity

2021 ◽  
Author(s):  
Sepideh Bakhoda ◽  
Thomas Thiemann
Keyword(s):  
Gauge Theory ◽  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Hamiltonian Formulation ◽  
The Other ◽  
Topological Theory ◽  
Yang Mills ◽  
Consistent Model ◽  
Starting Point ◽  
Euclidean Signature

Abstract If one replaces the constraints of the Ashtekar-Barbero $SU(2)$ gauge theory formulation of Euclidean gravity by their $U(1)^3$ version, one arrives at a consistent model which captures significant structures of its $SU(2)$ version. In particular, it displays a non-trivial realisation of the hypersurface deformation algebra which makes it an interesting testing ground for (Euclidean) quantum gravity as has been emphasised in a recent series of papers due to Varadarajan et al. The simplification from SU(2) to U(1)$^3$ can be performed simply by hand within the Hamiltonian formulation by dropping all non-Abelian terms from the Gauss, spatial diffeomorphism, and Hamiltonian constraints respectively. However, one may ask from which Lagrangian formulation this theory descends. For the SU(2) theory it is known that one can choose the Palatini action, Holst action, or (anti-)selfdual action (Euclidean signature) as starting point all leading to equivalent Hamiltonian formulations. In this paper, we systematically analyse this question directly for the U(1)$^3$ theory. Surprisingly, it turns out that the Abelian analog of the Palatini or Holst formulation is a consistent but topological theory without propagating degrees of freedom. On the other hand, a twisted Abelian analog of the (anti-)selfdual formulation does lead to the desired Hamiltonian formulation. A new aspect of our derivation is that we work with 1. half-density valued tetrads which simplifies the analysis, 2. without the simplicity constraint (which admits one undesired solution that is usually neglected by hand) and 3. without imposing the time gauge from the beginning. As a byproduct, we show that also the non-Abelian theory admits a twisted (anti-)selfdual formulation. Finally, we also derive a pure connection formulation of Euclidean GR including a cosmological constant by extending previous work due to Capovilla, Dell, Jacobson, and Peldan which may be an interesting starting point for path integral investigations and displays (Euclidean) GR as a Yang-Mills theory with non-polynomial Lagrangian.

scholarly journals A QUANTUM-GRAVITY PERSPECTIVE ON SEMICLASSICAL vs. STRONG-QUANTUM DUALITY

2006 ◽  
Vol 03 (07) ◽  
pp. 1293-1302
Author(s):  
JOSÉ M. ISIDRO
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
The Other ◽  
Length Scale ◽  
Specific Nature ◽  
Action Integral ◽  
Fundamental Length ◽  
Starting Point ◽  
Duality Groups ◽  
Quantum Duality

It has been argued that, underlying the M-theoretic dualities, there should exist a symmetry relating the semiclassical and the strong-quantum regimes of a given action integral. On the other hand, a field-theoretic exchange between long and short distances (similar in nature to the T-duality of strings) has been shown to provide a starting point for quantum gravity, in that this exchange enforces the existence of a fundamental length scale on spacetime. In this paper, we prove that the above semiclassical vs. strong-quantum symmetry is equivalent to the exchange of long and short distances. Hence the former symmetry, as much as the latter, also enforces the existence of a length scale. We apply these facts in order to classify all possible duality groups of a given action integral on spacetime, regardless of its specific nature and of its degrees of freedom.

Extended Vacuum Solutions and their Elementary Excitations of the Yang–Mills Gauge Theory

1997 ◽  
Vol 12 (27) ◽  
pp. 2037-2045
Author(s):  
T. Tajima ◽  
Q. Niu
Keyword(s):  
Magnetic Field ◽  
Gauge Theory ◽  
Constant Magnetic Field ◽  
Vacuum Solution ◽  
Landau Levels ◽  
The Other ◽  
Elementary Excitations ◽  
Circularly Polarized ◽  
Yang Mills ◽  
Vacuum Solutions

A number of nontrivial vacua of the Yang–Mills gauge theory which are extended in space are derived. For the vacuum solution with a constant "magnetic" field of one color species, the elementary excitations of the other species are circularly polarized, with a spectrum much like the Landau levels of nonrelativistic electrons in a constant magnetic field.

scholarly journals The Fröhlich-Morchio-Strocchi mechanism and quantum gravity

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Axel Maas
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Quantum Field ◽  
Yang Mills ◽  
Guiding Principle ◽  
Quantum Numbers ◽  
Gravity Fields ◽  
Physical Spectrum ◽  
Physical Objects

Taking manifest invariance under both gauge symmetry and diffeomorphisms as a guiding principle physical objects are constructed for Yang-Mills-Higgs theory coupled to quantum gravity. These objects are entirely classified by quantum numbers defined in the tangent space. Applying the Fröhlich-Morchio-Strocchi mechanism to these objects reveals that they coincide with ordinary correlation functions in quantum-field theory, if quantum fluctuations of gravity and curvature become small. Taking these descriptions literally exhibits how quantum gravity fields need to dress quantum fields to create physical objects, i. e. giving a graviton component to ordinary observed particles. The same mechanism provides access to the physical spectrum of pure gravitational degrees of freedom.

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.

NON-COMMUTATIVE GAUGE THEORY ON FUZZY ℂP2

2005 ◽  
Vol 20 (17n18) ◽  
pp. 1345-1357
Author(s):  
HAROLD STEINACKER
Keyword(s):  
Gauge Theory ◽  
Path Integral ◽  
Matrix Model ◽  
Degrees Of Freedom ◽  
Finite Size ◽  
Gauge Fields ◽  
Auxiliary Variables ◽  
Hermitian Matrices ◽  
Yang Mills ◽  
Classical Symmetries

Gauge theory on fuzzy ℂP2 can be defined as a multi-matrix model, which consistently combines a UV cutoff with the classical symmetries of ℂP2. The degrees of freedom are 8 hermitian matrices of finite size, 4 of which are tangential gauge fields and 4 are auxiliary variables. The model depends on a noncommutativity parameter [Formula: see text], and reduces to the usual U(n) Yang-Mills action on the 4-dimensional classical ℂP2 in the limit N→∞. The quantization of the model is defined in terms of a path integral, which is manifestly finite.

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

scholarly journals From Center-Vortex Ensembles to the Confining Flux Tube

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 253
Author(s):  
David R. Junior ◽  
Luis E. Oxman ◽  
Gustavo M. Simões
Keyword(s):  
Degrees Of Freedom ◽  
String Tension ◽  
Effective Field ◽  
Scaling Properties ◽  
Flux Tubes ◽  
Topological Solitons ◽  
Yang Mills ◽  
Center Vortex ◽  
Asymptotic Scaling ◽  
The Continuum

In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the non-oriented center-vortex component and non-Abelian degrees of freedom when modeling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.

scholarly journals Scrambling in Yang-Mills

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Robert de Mello Koch ◽  
Eunice Gandote ◽  
Augustine Larweh Mahu
Keyword(s):  
Relaxation Time ◽  
Weak Coupling ◽  
Degrees Of Freedom ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Dilatation Operator ◽  
Super Yang Mills Theory

Abstract Acting on operators with a bare dimension ∆ ∼ N2 the dilatation operator of U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory defines a 2-local Hamiltonian acting on a graph. Degrees of freedom are associated with the vertices of the graph while edges correspond to terms in the Hamiltonian. The graph has p ∼ N vertices. Using this Hamiltonian, we study scrambling and equilibration in the large N Yang-Mills theory. We characterize the typical graph and thus the typical Hamiltonian. For the typical graph, the dynamics leads to scrambling in a time consistent with the fast scrambling conjecture. Further, the system exhibits a notion of equilibration with a relaxation time, at weak coupling, given by t ∼ $$ \frac{\rho }{\lambda } $$ ρ λ with λ the ’t Hooft coupling.

scholarly journals Real-time simulation of (2+1)-dimensional lattice gauge theory on qubits

2020 ◽  
Author(s):  
Arata Yamamoto
Keyword(s):  
Gauge Theory ◽  
Real Time ◽  
Degrees Of Freedom ◽  
Quantum Computer ◽  
Lattice Gauge Theory ◽  
Dual Variable ◽  
Dimensional Lattice ◽  
The Real ◽  
Lattice Gauge ◽  
Time Simulation

Abstract We study the quantum simulation of Z2 lattice gauge theory in 2+1 dimensions. The dual variable formulation, the so-called Wegner duality, is utilized for reducing redundant gauge degrees of freedom. The problem of artificial charge unconservation is resolved for any charge distribution. As a demonstration, we simulate the real-time evolution of the system with two static electric charges, i.e., with two temporal Wilson lines. Some results obtained by the simulator (with no hardware noise) and the real device (with sizable hardware noise) of a quantum computer are shown.

Ontology and Perception

2004 ◽  
Vol 5 (1) ◽  
pp. 43-58
Author(s):  
Jeffrey S. Galko ◽  
Keyword(s):  
Common Sense ◽  
The Other ◽  
Cognitive Capacity ◽  
Complex Environment ◽  
Starting Point ◽  
Ontological Question ◽  
The One ◽  
Bodies Of Water ◽  
The Relationship

The ontological question of what there is, from the perspective of common sense, is intricately bound to what can be perceived. The above observation, when combined with the fact that nouns within language can be divided between nouns that admit counting, such as ‘pen’ or ‘human’, and those that do not, such as ‘water’ or ‘gold’, provides the starting point for the following investigation into the foundations of our linguistic and conceptual phenomena. The purpose of this paper is to claim that such phenomena are facilitated by, on the one hand, an intricate cognitive capacity, and on the other by the complex environment within which we live. We are, in a sense, cognitively equipped to perceive discrete instances of matter such as bodies of water. This equipment is related to, but also differs from, that devoted to the perception of objects such as this computer. Behind this difference in cognitive equipment underlies a rich ontology, the beginnings of which lies in the distinction between matter and objects. The following paper is an attempt to make explicit the relationship between matter and objects and also provide a window to our cognition of such entities.

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