4 research outputs found
Rotor Spectra and Berry Phases in the Chiral Limit of QCD on a Torus
We consider the finite-volume spectra of QCD in the chiral limit of massless
up and down quarks and massive strange quarks in the baryon number sectors and for different values of the isospin. Spontaneous symmetry
breaking gives rise to rotor spectra, as the chiral order parameter precesses
through the vacuum manifold. Baryons of different isospin influence the motion
of the order parameter through non-trivial Berry phases and associated abstract
monopole fields. Our investigation provides detailed insights into the dynamics
of spontaneous chiral symmetry breaking in QCD on a torus. It also sheds new
light on Berry phases in the context of quantum field theory. Interestingly,
the Berry gauge field resulting from QCD solves a Yang-Mills-Chern-Simons
equation of motion on the vacuum manifold .Comment: 21 pages, 3 figures. Revised version: Slightly expanded introduction
and conclusion, a few references adde
Doubled lattice Chern–Simons–Yang–Mills theories with discrete gauge group
We construct doubled lattice Chern–Simons–Yang–Mills theories with discrete gauge group G in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov–Bohm phase, which is manifested in the doubled theory in terms of a nontrivial ground-state degeneracy on a single cross. We discuss several examples of these doubled theories with different gauge groups including the cyclic group Z(k)⊂U(1), the symmetric group S3⊂O(2), the binary dihedral (or quaternion) group View the MathML source, and the finite group Δ(27)⊂SU(3). In each case the spectrum of the single-cross electric Hamiltonian is determined exactly. We examine the nature of the low-lying excited states in the full Hilbert space, and emphasize the role of the center symmetry for the confinement of charges. Whether the investigated doubled models admit a non-Abelian topological state which allows for fault-tolerant quantum computation will be addressed in a future publication
The Aharonov-Bohm effect in conical space
Conical space emerges inevitably as an outer space of any topological defect
of the vortex type. Quantum-mechanical scattering of a nonrelativistic particle
by a vortex centred in conical space is considered, and effects of the
transverse size of the vortex are taken into account. Paradoxical peculiarities
of scattering in the short-wavelength limit are discussed.Comment: 17 pages, 2 figures, minor change