Related papers: Symmetry Breaking and Lattice Kirigami
The widespread belief that the effective action is convex and has a flat bottom under broken global symmetry is shown to be wrong. We show spontaneous symmetry breaking necessarily accompanies non-convexity in the effective action for…
Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space…
We study supersymmetry breaking effects in N=1 SYM from the point of view of quantum effective actions. Restrictions on the geometry of the effective potential from superspace are known to be problematic in quantum effective actions, where…
Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semi-simple Lie algebras with respect to formal deformations is…
Perhaps the most important aspect of symmetry in physics is the idea that a state does not need to have the same symmetries as the theory that describes it. This phenomenon is known as spontaneous symmetry breaking. In these lecture notes,…
We study phase transition behavior of the Heisenberg model on a distorted triangular lattice with competing interactions. The ground-state phase diagram indicates that underlying symmetry can be changed by tuning parameters. We focus on two…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…
We construct lattice gauge field theory based on a quantum group on a lattice of dimension 1. Innovations include a coalgebra structure on the connections, and an investigation of connections that are not distinguishable by observables. We…
The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's…
A spontaneous symmetry breaking mechanism is used in quantum gravity to obtain a convergent positive definite density-matrix as the most general quantum state of Euclidean wormholes
We study some basic quantum confinement effects through investigation a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation function within the…
The lattice definition of the two-dimensional topological quantum field theory [Fukuma, {\em et al}, Commun.~Math.~Phys.\ {\bf 161}, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that…
Spontaneous symmetry breaking has revolutionized the understanding in numerous fields of modern physics. Here, we theoretically demonstrate the spontaneous time-reversal symmetry breaking in a cavity quantum electrodynamics system in which…
A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite…
In this dissertation, we study the implications generated by the Lorentz breaking symmetry in quantum electrodynamics. We analyze fermions interacting with an electromagnetic field in the contexts of quantum mechanics and make radiative…
We present some new ideas on how to design analogue models of quantum fields living in curved spacetimes using ultra-cold atoms in optical lattices. We discuss various types of static and dynamical curved spacetimes achievable by simple…
We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…
A q-deformed two-dimensional phase space is studied as a model for a noncommutative phase space. A lattice structure arises that can be interpreted as a spontaneous breaking of a continuous symmetry. The eigenfunctions of a Hamiltonian that…
The technique of damage spreading is used to study the phase diagram of the easy axis anisotropic Heisenberg antiferromagnet on two geometrically frustrated lattices. The triangular and kagome systems are built up from triangular units that…
A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to…