Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 54, Issue 11, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/abe310
Keywords
discrete Lorentz symmetry; quantum lattice theory; discrete spacetime translational symmetry; representation of group
Categories
Funding
- NSFC [11774315, 11835011]
- Junior Associates program of the Abdus Salam International Center for Theoretical Physics
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The paper develops a quantum theory with discrete Poincare symmetry on a one-dimensional Bravais lattice and establishes a Lorentz-invariant many-body theory for indistinguishable particles. It analyzes typical Hamiltonians and calculates the Green's function.
In this paper, we develop the quantum theory that has discrete Poincare symmetry on the one-dimensional Bravais lattice. We review the recently discovered discrete Lorentz symmetry which coexists with the discrete space translational symmetry on a Bravais lattice. The discrete Lorentz transformations and spacetime translations form the discrete Poincare group, which are represented by unitary operators in a quantum theory. We find the conditions for the existence of representation, which are expressed as the congruence relation between quasi-momentum and quasi-energy. We then build the Lorentz-invariant many-body theory of indistinguishable particles by expressing both the unitary operators and Floquet Hamiltonians in terms of the field operators. Some typical Hamiltonians include the long-range hopping which fluctuates as the distance between sites increases. We calculate the Green's function of the theory. The spacetime points where the Green's function is nonzero display a lattice structure. During the propagation, the particle stays localized on a single or a few sites to preserve the Lorentz symmetry.
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