scholarly journals On the Minimal Length Uncertainty Relation and the Foundations of String Theory

2011 ◽  
Vol 2011 ◽  
pp. 1-30 ◽  
Author(s):  
Lay Nam Chang ◽  
Zachary Lewis ◽  
Djordje Minic ◽  
Tatsu Takeuchi
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
String Theory ◽  
Momentum Space ◽  
Vacuum Energy ◽  
Uncertainty Relation ◽  
Minimal Length

We review our work on the minimal length uncertainty relation as suggested by perturbative string theory. We discuss simple phenomenological implications of the minimal length uncertainty relation and then argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy-momentum space. We discuss the implication of this for the problem of vacuum energy and the foundations of nonperturbative string theory.

scholarly journals WHY THERE IS SOMETHING SO CLOSE TO NOTHING: TOWARDS A FUNDAMENTAL THEORY OF THE COSMOLOGICAL CONSTANT

2007 ◽  
Vol 22 (10) ◽  
pp. 1797-1818 ◽  
Author(s):  
VISHNU JEJJALA ◽  
DJORDJE MINIC
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Uncertainty Relation ◽  
Space Time ◽  
Large Size ◽  
Minkowski Space Time ◽  
The Universe ◽  
Canonical Quantum

The cosmological constant problem is turned around to argue for a new foundational physics postulate underlying a consistent quantum theory of gravity and matter, such as string theory. This postulate is a quantum equivalence principle which demands a consistent gauging of the geometric structure of canonical quantum theory. We argue that string theory can be formulated to accommodate such a principle, and that in such a theory the observed cosmological constant is a fluctuation about a zero value. This fluctuation arises from an uncertainty relation involving the cosmological constant and the effective volume of space–time. The measured, small vacuum energy is dynamically tied to the large "size" of the universe, thus violating naive decoupling between small and large scales. The numerical value is related to the scale of cosmological supersymmetry breaking, supersymmetry being needed for a nonperturbative stability of local Minkowski space–time regions in the classical regime.

scholarly journals QUANTUM GRAVITY, DYNAMICAL ENERGY–MOMENTUM SPACE AND VACUUM ENERGY

2010 ◽  
Vol 25 (35) ◽  
pp. 2947-2954 ◽  
Author(s):  
LAY NAM CHANG ◽  
DJORDJE MINIC ◽  
TATSU TAKEUCHI
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Momentum Space ◽  
Vacuum Energy

We argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy–momentum space. We discuss the freezing of vacuum energy in such a dynamical energy–momentum space and present a phenomenologically viable seesaw formula for the cosmological constant in this context.

scholarly journals Quantum gravity, dynamical phase-space and string theory

2014 ◽  
Vol 23 (12) ◽  
pp. 1442006 ◽  
Author(s):  
Laurent Freidel ◽  
Robert G. Leigh ◽  
Djordje Minic
Keyword(s):  
Quantum Theory ◽  
Phase Space ◽  
String Theory ◽  
Quantum Gravity ◽  
Momentum Space ◽  
Symplectic Geometry ◽  
Complex Geometry ◽  
Hamiltonian Dynamics ◽  
Natural Extension ◽  
Dynamical Phase

In a natural extension of the relativity principle, we speculate that a quantum theory of gravity involves two fundamental scales associated with both dynamical spacetime as well as dynamical momentum space. This view of quantum gravity is explicitly realized in a new formulation of string theory which involves dynamical phase-space and in which spacetime is a derived concept. This formulation naturally unifies symplectic geometry of Hamiltonian dynamics, complex geometry of quantum theory and real geometry of general relativity. The spacetime and momentum space dynamics, and thus dynamical phase-space, is governed by a new version of the renormalization group (RG).

scholarly journals The Quantum Cosmological Constant

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1130 ◽  
Author(s):  
Stephon Alexander ◽  
Joao Magueijo ◽  
Lee Smolin
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Uncertainty Relation ◽  
Time Variable ◽  
Transition Functions ◽  
New Interpretation ◽  
Chern Simons

We present an extension of general relativity in which the cosmological constant becomes dynamical and turns out to be conjugate to the Chern–Simons invariant of the Ashtekar connection on a spatial slicing. The latter has been proposed Soo and Smolin as a time variable for quantum gravity: the Chern–Simons time. In the quantum theory, the inverse cosmological constant and Chern–Simons time will then become conjugate operators. The “Kodama state” gets a new interpretation as a family of transition functions. These results imply an uncertainty relation between Λ and Chern–Simons time; the consequences of which will be discussed elsewhere.

scholarly journals Minimal Length and the Existence of Some Infinitesimal Quantities in Quantum Theory and Gravity

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
A. E. Shalyt-Margolin
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Minimal Length ◽  
Low Energy ◽  
Mathematical Apparatus ◽  
Holographic Screen ◽  
Energy Theory

It is demonstrated that provided a theory involves a minimal length, this theory must be free from such infinitesimal quantities as infinitely small variations in surface of the holographic screen, its volume, and entropy. The corresponding infinitesimal quantities in this case must be replaced by the “minimal variations possible”—finite quantities dependent on the existent energies. As a result, the initial low-energy theory (quantum theory or general relativity) inevitably must be replaced by a minimal length theory that gives very close results but operates with absolutely other mathematical apparatus.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

Between general relativity and quantum theory

1982 ◽  
Vol 14 (11) ◽  
pp. 1085-1093
Author(s):  
Jerzy Rayski
Keyword(s):  
General Relativity ◽  
Quantum Theory

ONE-LOOP VACUUM ENERGY AT THE TACHYON VACUUM

2013 ◽  
Vol 21 ◽  
pp. 157-158
Author(s):  
SHOKO INATOMI
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
String Field Theory ◽  
Vacuum Energy ◽  
Open String ◽  
Brst Operator ◽  
Identity Based ◽  
Homotopy Operators

We consider one-loop vacuum energy at the tachyon vacuum in cubic bosonic open string field theory. The BRST operator Ql in the theory around an identity-based solution is believed to represent a kinetic operator at the tachyon vacuum. Using homotopy operators for Ql, we find that one-loop vacuum energy at the tachyon vacuum is independent of moduli such as interbrane distances. This result can be interpreted as support for the annihilation of D-branes at the tachyon vacuum even in the quantum theory.

GEOMETRY OF SPACETIME AND FINSLER GEOMETRY

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1678-1685 ◽  
Author(s):  
REZA TAVAKOL
Keyword(s):  
General Relativity ◽  
String Theory ◽  
Riemannian Geometry ◽  
Lorentz Invariance ◽  
Finsler Geometry ◽  
Spacetime Geometry ◽  
Test Particles ◽  
Light Rays ◽  
Recent Developments ◽  
Underlying Geometry

A central assumption in general relativity is that the underlying geometry of spacetime is pseudo-Riemannian. Given the recent attempts at generalizations of general relativity, motivated both by theoretical and observational considerations, an important question is whether the spacetime geometry can also be made more general and yet still remain compatible with observations? Here I briefly summarize some earlier results which demonstrate that there are special classes of Finsler geometry, which is a natural metrical generalization of the Riemannian geometry, that are strictly compatible with the observations regarding the motion of idealised test particles and light rays. I also briefly summarize some recent attempts at employing Finsler geometries motivated by more recent developments such as those in String theory, whereby Lorentz invariance is partially broken.

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