A Lesson from the LQG String: Diffeomorphism Covariance is Enough

Journal Article · Tue Dec 15 00:00:00 EST 2009 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3284378· OSTI ID:21371371

Helling, Robert C ^[1]

---

1. Arnold Sommerfeld Center, Ludwig-Maximilians-Universitaet Muenchen, Theresienstrasse 37, D-80333 Muenchen (Germany)

The importance of manifest diffeomorphism invariance is often cited as a major strength of the loop approach to the quantization of gravity. We study this in a simple example: The world-sheet theory of the bosonic string. The conventional treatment differs in the choice of vacuum state from the loop inspired one, the latter being invariant while the first being only covariant. We argue that physically only covariance is required and display the physical consequences of the invariant but discontinuous choice in the one dimensional example of the harmonic oscillator. Finally, we demonstrate that discretization of infinitesimally singular expressions as common in the loop approach is not unique but can be seen in analogy with the choice of higher derivative counter terms.

• OSTI ID: 21371371
• Journal Information: AIP Conference Proceedings, Vol. 1196, Issue 1; Conference: 25. Max Born symposium, Wroclaw (Poland), 29 Jun - 3 Jul 2009; Other Information: DOI: 10.1063/1.3284378; (c) 2009 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
GRAVITATION
HARMONIC OSCILLATORS
HILBERT SPACE
LIE GROUPS
ONE-DIMENSIONAL CALCULATIONS
QUANTIZATION
QUANTUM GRAVITY
STRING MODELS
STRING THEORY
VACUUM STATES
BANACH SPACE
COMPOSITE MODELS
EXTENDED PARTICLE MODEL
FIELD THEORIES
MATHEMATICAL MODELS
MATHEMATICAL SPACE
M-THEORY
PARTICLE MODELS
QUANTUM FIELD THEORY
QUARK MODEL
SPACE
SYMMETRY GROUPS