Related papers: Counting Rules of Nambu-Goldstone Modes
I begin these lectures by examining the transformation properties of quantum fields under the discrete symmetries of Parity, P, Charge Conjugation, C, and Time Reversal, T. With these results in hand, I then show how the structure of the…
We introduce a lattice fermion model in one spatial dimension with supersymmetry (SUSY) but without particle number conservation. The Hamiltonian is defined as the anticommutator of two nilpotent supercharges $Q$ and $Q^\dagger$. Each…
Some important rigorous results on phase transitions accompanied by the spontaneous breaking of symmetries in statistical mechanics and relativistic quantum field theory are reviewed. Basic ideas, mainly inspired by quantum field theory,…
Multi-gap superconductors exhibit interesting properties. In an $N$-gap superconductor, we have in general $U(1)^N$ phase invariance. This multiple-phase invariance is partially or totally spontaneously broken in a superconductor. The…
In this work we study spontaneous symmetry breaking patterns in tensor models. We focus on the patterns which lead to effective matrix theories transforming in the adjoint of $U(N)$. We find the explicit form of the Goldstone bosons which…
We study the dynamics of spontaneous translation symmetry breaking in holographic models in presence of weak explicit sources. We show that, unlike conventional gapped quantum charge density wave systems, this dynamics is well characterized…
We discuss selected aspects of classical relativistic scalar field theories with nonzero chemical potential. First, we offer a review of classical field theory at nonzero density within the Lagrangian formalism. The aspects covered include…
We consider some aspects of spontaneous breaking of Lorentz Invariance in field theories, discussing the possibility that the certain tensor operators may condensate in the ground state in which case the tensor Goldstone particles would…
Higgs bosons - the amplitude modes - have been experimentally investigated in condensed matter for many years. An example is superfluid $^3$He-B, where the broken symmetry leads to 4 Goldstone modes and at least 14 Higgs modes, which are…
We study a system involving a single quantum degree of freedom per site of the lattice interacting with a few neighbors (up to second neighbors), with the interactions chosen as to produce frustration. At zero temperature, this system…
A new mechanism for breaking an internal symmetry spontaneously is discussed, which is intermediate between the Nambu-Goldstone and Wigner modes of symmetry breaking. Here the quark-antiquark sea takes the role of the vacuum of the…
Finite group symmetry is commonplace in Physics, in particular through crystallographic groups occurring in condensed matter physics -- but also through the inversions (C,P,T and their combinations) occurring in high energy physics and…
Violations of spacetime symmetries have recently been identified as promising signatures for physics underlying the Standard Model. The present talk gives an overview over various topics in this field: The motivations for spacetime-symmetry…
We construct a non-linear electrodynamics arising from the spontaneous Lorentz symmetry breaking triggered by a non-zero vacuum expectation value of the electromagnetic field strength, instead of the electromagnetic potential. The expansion…
We construct the Wess-Zumino terms from anomalies in case of quasigroups for the following situations. One is effective gauge field theories of Nambu-Goldstone fields associated with spontaneously broken global symmetries and the other is…
We consider a quantum many-body system on a lattice with a continuous symmetry which exhibits a spontaneous symmetry breaking in its infinite volume ground states, but in which the order operator does not commute with the Hamiltonian. A…
We study a lattice Nambu-Jona-Lasinio model with SU(2) and SU(3) flavor symmetries of staggered fermions in the Kogut-Susskind Hamiltonian formalism. This type of four-fermion interactions has been widely used for describing low-energy…
We describe an algebraic framework for studying the symmetry properties of integrable quantum systems on the half line. The approach is based on the introduction of boundary operators. It turns out that these operators both encode the…
We outline a scenario where both the Higgs and a complex scalar dark matter candidate arise as the pseudo-Nambu-Goldstone bosons of breaking a global $SO(7)$ symmetry to $SO(6)$. The novelty of our construction is that the symmetry partners…
We discuss the spontaneous symmetry breaking (SSB) on the light front (LF) in view of the zero mode. We first demonstrate impossibility to remove the zero mode in the continuum LF theory by two examples: The Lorentz invariance forbids even…