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Title: Lattice Dirac fermions on a simplicial Riemannian manifold

Authors:
; ; ; ; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1366329
Grant/Contract Number:
SC0015845; Sc0010010-Task-A
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 95; Journal Issue: 11; Related Information: CHORUS Timestamp: 2017-06-23 22:12:50; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English

Citation Formats

Brower, Richard C., Weinberg, Evan S., Fleming, George T., Gasbarro, Andrew D., Raben, Timothy G., and Tan, Chung-I. Lattice Dirac fermions on a simplicial Riemannian manifold. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.95.114510.
Brower, Richard C., Weinberg, Evan S., Fleming, George T., Gasbarro, Andrew D., Raben, Timothy G., & Tan, Chung-I. Lattice Dirac fermions on a simplicial Riemannian manifold. United States. doi:10.1103/PhysRevD.95.114510.
Brower, Richard C., Weinberg, Evan S., Fleming, George T., Gasbarro, Andrew D., Raben, Timothy G., and Tan, Chung-I. Fri . "Lattice Dirac fermions on a simplicial Riemannian manifold". United States. doi:10.1103/PhysRevD.95.114510.
@article{osti_1366329,
title = {Lattice Dirac fermions on a simplicial Riemannian manifold},
author = {Brower, Richard C. and Weinberg, Evan S. and Fleming, George T. and Gasbarro, Andrew D. and Raben, Timothy G. and Tan, Chung-I},
abstractNote = {},
doi = {10.1103/PhysRevD.95.114510},
journal = {Physical Review D},
number = 11,
volume = 95,
place = {United States},
year = {Fri Jun 23 00:00:00 EDT 2017},
month = {Fri Jun 23 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on June 23, 2018
Publisher's Accepted Manuscript

Citation Metrics:
Cited by: 1work
Citation information provided by
Web of Science

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  • We define the simplicial analogues of two concepts from differential topology: the concept of a point on the simplicial manifold and the concept of a tangent space on a simplicial manifold. We derive the simplicial analogues of parallel transport, the covariant derivative, connections, the Riemann curvature tensor, and the Einstein tensor. We construct the extrinsic curvature for a simplicial hypersurface using the simplicial covariant derivative. We discuss the importance of this simplicial extrinsic curvature to the 3+1 Regge-calculus program. It appears to us that the newly developed null-strut lattice is the most natural version of a 3+1 Regge lattice formore » the construction of extrinsic curvature. (A null-strut lattice is a 3+1 Regge spacetime lattice with TrK = const simplicial hypersurfaces, each connected to its two adjacent hypersurfaces entirely by simplicial light cones built of null struts.) Finally, we test the Regge-calculus version of the extrinsic curvature on a Bianchi type-IX simplicial hypersurface. The calculation agrees with the continuum expression to first order.« less
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  • The geometrical properties of a flat tangent space-time local to the manifold of the Einstein--Schroedinger nonsymmetric theory to which an internal octonionic space is attached, is developed here. As an application of the theory, an octonionic Dirac equation for a spin-1/2 particle is also obtained, where is now used an octonionic-like gauge field. It is shown that the (quaternionic) nonsymmetric Yang--Mills theory can be easily recovered and from there, the usual gauge theory on a curved space.
  • The Dirac wave equation is obtained in the non-Riemannian manifold of the Einstein--Schroedinger nonsymmetric theory. A new internal connection is determined in terms of complex vierbeins, which shows the coupling of the electromagnetic potential with gravity in the presence of a spin- 1/2 field.
  • I show how to avoid a two level nested conjugate gradient procedure in the context of a hybrid Monte Carlo algorithm with the overlap fermionic action. The resulting procedure is quite similar to a hybrid Monte Carlo algorithm with domain wall fermions, but is more flexible and therefore has some potential worth exploring. [copyright] [ital 1999] [ital The American Physical Society]