Related papers: Parity and CT realization in QCD
Von Neumann use 4 assumptions to derive the Hilbert space (HS) formulation of quantum mechanics (QM). Within this theory dispersion free ensembles do not exist. To accommodate a theory of quantum mechanics that allow dispersion free…
The Einstein-Cartan theory of gravity can arise from a mechanism of spontaneous symmetry breaking within the context of pre-geometric gauge theories. In this work, we develop the Hamiltonian analysis of such theories. By making contact with…
We discuss the BCF anomaly of massless QCD-like theories, first obtained by Anber and Poppitz, from the viewpoint of the low energy effective theories. We assume that the QCD-like theories exhibit spontaneous chiral symmetry breaking due to…
It is believed that unbroken PT symmetry is sufficient to guarantee that the spectrum of a non-Hermitian Hamiltonian is real. We prove that this is not true. We study a Hamiltonian with complex spectrum for which PT symmetry is not…
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully…
We determine the patterns of spontaneous symmetry breaking in strong-coupling lattice QCD in a fixed background baryon density. We employ a next-nearest-neighbor fermion formulation that possesses the SU(N_f)xSU(N_f) chiral symmetry of the…
We prove the conjecture proposed by Hartman, Keller and Stoica [HKS14]: the grand-canonical free energy of a unitary 2D CFT with a sparse spectrum below the scaling dimension $\frac{c}{12}+\epsilon$ and below the twist $\frac{c}{12}$ is…
Currently there is much interest in Hamiltonians that are not Hermitian but instead possess an antilinear $PT$ symmetry, since such Hamiltonians can still lead to the time-independent evolution of scalar products, and can still have an…
We give a pedagogical review of implications of chiral symmetry in QCD. First, we briefly discuss classical textbook subjects such as the axial anomaly, spontaneous breaking of the flavor-nonsinglet chiral symmetry, formation of light…
The Quantum Ergodic Conjecture equates the Wigner function for a typical eigenstate of a classically chaotic Hamiltonian with a delta-function on the energy shell. This ensures the evaluation of classical ergodic expectations of simple…
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…
We discuss the vacuum structure of $\phi^4$-theory in 1+1 dimensions quantised on the light-front $x^+ =0$. To this end, one has to solve a non-linear, operator-valued constraint equation. It expresses that mode of the field operator having…
The vacuum of quantum fields contains correlated fluctuations. When restricted to one side of a surface these have a huge entropy of entanglement that scales with the surface area. If UV physics renders this entropy finite, then a…
Pseudo-Hermitian (including $\mathcal{PT}$-symmetric) field theories support phenomenology that cannot be replicated in standard Hermitian theories. We describe a concrete example in which the vortex solutions that are realised in a…
Symmetries in Quantum Field Theory may have 't Hooft anomalies. If the symmetry is unbroken in the vacuum, the anomaly implies a nontrivial low-energy limit, such as gapless modes or a topological field theory. If the symmetry is…
In a previous paper [9], we proved the following singularity theorem applicable to cosmological models with a positive cosmological constant: if a four-dimensional spacetime satisfying the null energy condition contains a compact Cauchy…
General relativity, despite its profound successes, fails as a complete theory due to presence of singularities. While it is widely believed that quantum gravity has the potential to be a complete theory, in which spacetime consistently…
This study demonstrates that the common practice of determining spontaneous Lorentz violation via the minimum of a Lagrangian potential is generally incorrect. By analyzing the Hamiltonian structure and constraints of vector fields, we show…
We study spontaneous symmetry breaking in phi^4_(1+1) using the light-front formulation of the field theory. Since the physical vacuum is always the same as the perturbative vacuum in light-front field theory the fields must develop a…
In absence of matter Einstein gravity with a cosmological constant $\La$ can be formulated as a scale-free theory depending only on the dimensionless coupling constant G \Lambda where G is Newton constant. We derive the conformal field…