Quantization of 1+1 Dimensional Horava-Lifshitz Gravity

ORAL

Abstract

we study the quantization of the (1+1)-dimensional projectable Horava-Lifshitz gravity, and find that, when only gravity is present, the system can be quantized by following the standard Dirac quantization. The corresponding Hamilton can also be written in terms of a simple harmonic oscillator, where the expectation value of the gauge-invariant length operator defines the fundamental length of the system. When the gravity minimally couples to a scalar field, the momentum constraint can be solved explicitly only in the case where the fundamental variables are functions of time only. In this case, the coupled system can also be quantized by following the Dirac process. When the self-interaction of the scalar field vanishes, the corresponding Hamilton can be written in terms of two harmonic oscillators, one has positive energy, while the other has negative energy. A remarkable feature is that the space-time is well quantized, even when it is classically singular.

–

Authors

  • Baofei Li

    baylor university

  • Harry A. Atwater

    Institute for Advanced Physics and Mathematics, Zhejiang University of Technology, Baylor University, baylor university, Lanzhou Jiaotong University, Lanzhou University, Trinity University, University of New Hampshire, Los Alamos National Lab, Southwest Research Institute, University of Texas San Antonio, Texas A&M University, Department of Physics, Texas State University, San Marcos, TX78666, None, Southern Illinois University, Carbondale, Illinois 62901, Beijing Computational Science Research Center, Beijing 100094, P.R. China, The State Key Laboratory of Quantum Optics and Quantum Optics Devices, China, COMSATS Institute of Information Technology, Islamabad, Pakistan, Lamar University, NIST, NIST Physical Measurement Laboratory,Thermodynamic Metrology Laboratory, Rice University, University of Texas at Rio Grande Valley, University of Texas at Dallas, Texas Tech University, Department of Physics and Astronomy, Texas A\&M University, Russian Quantum Center, Physics Department, International Laser Center, M.V. Lomonosov Moscow State University, Baylor University, Texas A&M University, Princeton University, Baylor University, Texas A&M University, Florida State University, Univ of Texas, Dallas, University of Texas Rio Grande Valley, University of Houston, Physics and Astronomy, Material Science and Eng,Texas A\&M University. WPI-Advanced Institute for Materials Research, Tohoku University, Sendai, Japan, Physics and Astronomy, Texas A\&M University, Material Science and Eng., Texas A\&M University, Texas Christian University, Utaca College, University of Texas at Arlington, Angelo State University Physics & Geosciences Department, Texas State University, Universidade Federal de Viçosa, Department of Physics, Lamar University, Texas Lutheran University, University of Oklahoma, Texas A&M University, Baylor University, Princeton University, Texas A&M University, Baylor University, Institute for Quantum Science and Engineering (IQSE) and Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, Texas A\&M University, Florida A&M University, Texas A&M University, Princeton University, Baylor University, Department of Physics and Astronomy, Texas A&M University, College Station, TX, Texas A&M University and Baylor University, Abilene Christian University, Michigan State University, Argonne National Laboratory, Southern Methodist University, University of Maryland, Baltimore County, Baltimore, MD 21250, Institute for Quantum Science and Engineering, Texas A&M University 4242 TAMU College Station, Texas 77843-4242, The Institute for Quantum Science and Engineering, Texas A&M University, Southern Nazarene University, Texas A&M University, Landau Institute for Theoretical Physics, University of Cologne, Department of Physics, The University of Texas at Dallas, 800 W. Campbell Rd., Richardson, Texas 75080, USA, Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA, $^{1}$Department of Physics and Astronomy, Texas A\&M University, $^{1}$Department of Physics and Astronomy, Texas A\&M University, $^{2}$WPI-AIMR, Tohoku University, Japan, Department of Physics, Austin College, AMRIS/NHMFL, University of Florida, University of Texas Southwestern Medical Center, Mississippi State University, The Methodist Hospital System, Biophotonic Solutions, Inc., University of Texas, Austin, California Insititute of Technology

  • Harry A. Atwater

    Institute for Advanced Physics and Mathematics, Zhejiang University of Technology, Baylor University, baylor university, Lanzhou Jiaotong University, Lanzhou University, Trinity University, University of New Hampshire, Los Alamos National Lab, Southwest Research Institute, University of Texas San Antonio, Texas A&M University, Department of Physics, Texas State University, San Marcos, TX78666, None, Southern Illinois University, Carbondale, Illinois 62901, Beijing Computational Science Research Center, Beijing 100094, P.R. China, The State Key Laboratory of Quantum Optics and Quantum Optics Devices, China, COMSATS Institute of Information Technology, Islamabad, Pakistan, Lamar University, NIST, NIST Physical Measurement Laboratory,Thermodynamic Metrology Laboratory, Rice University, University of Texas at Rio Grande Valley, University of Texas at Dallas, Texas Tech University, Department of Physics and Astronomy, Texas A\&M University, Russian Quantum Center, Physics Department, International Laser Center, M.V. Lomonosov Moscow State University, Baylor University, Texas A&M University, Princeton University, Baylor University, Texas A&M University, Florida State University, Univ of Texas, Dallas, University of Texas Rio Grande Valley, University of Houston, Physics and Astronomy, Material Science and Eng,Texas A\&M University. WPI-Advanced Institute for Materials Research, Tohoku University, Sendai, Japan, Physics and Astronomy, Texas A\&M University, Material Science and Eng., Texas A\&M University, Texas Christian University, Utaca College, University of Texas at Arlington, Angelo State University Physics & Geosciences Department, Texas State University, Universidade Federal de Viçosa, Department of Physics, Lamar University, Texas Lutheran University, University of Oklahoma, Texas A&M University, Baylor University, Princeton University, Texas A&M University, Baylor University, Institute for Quantum Science and Engineering (IQSE) and Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, Texas A\&M University, Florida A&M University, Texas A&M University, Princeton University, Baylor University, Department of Physics and Astronomy, Texas A&M University, College Station, TX, Texas A&M University and Baylor University, Abilene Christian University, Michigan State University, Argonne National Laboratory, Southern Methodist University, University of Maryland, Baltimore County, Baltimore, MD 21250, Institute for Quantum Science and Engineering, Texas A&M University 4242 TAMU College Station, Texas 77843-4242, The Institute for Quantum Science and Engineering, Texas A&M University, Southern Nazarene University, Texas A&M University, Landau Institute for Theoretical Physics, University of Cologne, Department of Physics, The University of Texas at Dallas, 800 W. Campbell Rd., Richardson, Texas 75080, USA, Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA, $^{1}$Department of Physics and Astronomy, Texas A\&M University, $^{1}$Department of Physics and Astronomy, Texas A\&M University, $^{2}$WPI-AIMR, Tohoku University, Japan, Department of Physics, Austin College, AMRIS/NHMFL, University of Florida, University of Texas Southwestern Medical Center, Mississippi State University, The Methodist Hospital System, Biophotonic Solutions, Inc., University of Texas, Austin, California Insititute of Technology

  • Harry A. Atwater

    Institute for Advanced Physics and Mathematics, Zhejiang University of Technology, Baylor University, baylor university, Lanzhou Jiaotong University, Lanzhou University, Trinity University, University of New Hampshire, Los Alamos National Lab, Southwest Research Institute, University of Texas San Antonio, Texas A&M University, Department of Physics, Texas State University, San Marcos, TX78666, None, Southern Illinois University, Carbondale, Illinois 62901, Beijing Computational Science Research Center, Beijing 100094, P.R. China, The State Key Laboratory of Quantum Optics and Quantum Optics Devices, China, COMSATS Institute of Information Technology, Islamabad, Pakistan, Lamar University, NIST, NIST Physical Measurement Laboratory,Thermodynamic Metrology Laboratory, Rice University, University of Texas at Rio Grande Valley, University of Texas at Dallas, Texas Tech University, Department of Physics and Astronomy, Texas A\&M University, Russian Quantum Center, Physics Department, International Laser Center, M.V. Lomonosov Moscow State University, Baylor University, Texas A&M University, Princeton University, Baylor University, Texas A&M University, Florida State University, Univ of Texas, Dallas, University of Texas Rio Grande Valley, University of Houston, Physics and Astronomy, Material Science and Eng,Texas A\&M University. WPI-Advanced Institute for Materials Research, Tohoku University, Sendai, Japan, Physics and Astronomy, Texas A\&M University, Material Science and Eng., Texas A\&M University, Texas Christian University, Utaca College, University of Texas at Arlington, Angelo State University Physics & Geosciences Department, Texas State University, Universidade Federal de Viçosa, Department of Physics, Lamar University, Texas Lutheran University, University of Oklahoma, Texas A&M University, Baylor University, Princeton University, Texas A&M University, Baylor University, Institute for Quantum Science and Engineering (IQSE) and Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, Texas A\&M University, Florida A&M University, Texas A&M University, Princeton University, Baylor University, Department of Physics and Astronomy, Texas A&M University, College Station, TX, Texas A&M University and Baylor University, Abilene Christian University, Michigan State University, Argonne National Laboratory, Southern Methodist University, University of Maryland, Baltimore County, Baltimore, MD 21250, Institute for Quantum Science and Engineering, Texas A&M University 4242 TAMU College Station, Texas 77843-4242, The Institute for Quantum Science and Engineering, Texas A&M University, Southern Nazarene University, Texas A&M University, Landau Institute for Theoretical Physics, University of Cologne, Department of Physics, The University of Texas at Dallas, 800 W. Campbell Rd., Richardson, Texas 75080, USA, Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA, $^{1}$Department of Physics and Astronomy, Texas A\&M University, $^{1}$Department of Physics and Astronomy, Texas A\&M University, $^{2}$WPI-AIMR, Tohoku University, Japan, Department of Physics, Austin College, AMRIS/NHMFL, University of Florida, University of Texas Southwestern Medical Center, Mississippi State University, The Methodist Hospital System, Biophotonic Solutions, Inc., University of Texas, Austin, California Insititute of Technology