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.

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 The UV fate of anomalous U(1)s and the Swampland

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Nathaniel Craig ◽  
Isabel Garcia Garcia ◽  
Graham D. Kribs
Keyword(s):  
Quantum Gravity ◽  
Gauge Theories ◽  
Critical Size ◽  
Gauge Coupling ◽  
Low Energy ◽  
Gravitational Anomaly ◽  
Light Vector ◽  
Energy Theory ◽  
The Cost ◽  
Weak Gravity

Abstract Massive U(1) gauge theories featuring parametrically light vectors are suspected to belong in the Swampland of consistent EFTs that cannot be embedded into a theory of quantum gravity. We study four-dimensional, chiral U(1) gauge theories that appear anomalous over a range of energies up to the scale of anomaly-cancelling massive chiral fermions. We show that such theories must be UV-completed at a finite cutoff below which a radial mode must appear, and cannot be decoupled — a Stückelberg limit does not exist. When the infrared fermion spectrum contains a mixed U(1)-gravitational anomaly, this class of theories provides a toy model of a boundary into the Swampland, for sufficiently small values of the vector mass. In this context, we show that the limit of a parametrically light vector comes at the cost of a quantum gravity scale that lies parametrically below MP1, and our result provides field theoretic evidence for the existence of a Swampland of EFTs that is disconnected from the subset of theories compatible with a gravitational UV-completion. Moreover, when the low energy theory also contains a U(1)3 anomaly, the Weak Gravity Conjecture scale makes an appearance in the form of a quantum gravity cutoff for values of the gauge coupling above a certain critical size.

Between general relativity and quantum theory

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

scholarly journals NONCOMMUTATIVE OPEN STRING THEORIES AND THEIR DUALITIES

2001 ◽  
Vol 16 (04n06) ◽  
pp. 349-359 ◽  
Author(s):  
M. M. SHEIKH-JABBARI
Keyword(s):  
Open String ◽  
Low Energy ◽  
Duality Group ◽  
Critical Limit ◽  
Quantum Theories ◽  
Open Strings ◽  
Energy Theory ◽  
String Theories

The recently found noncritical open string theories is reviewed. These open strings, noncommutative open string theories (NCOS), arise as consistent quantum theories describing the low energy theory of D-branes in a background electric B-field in the critical limit. Focusing on the D3-brane case, we construct the most general (3+1) NCOS, which is described by four parameters. We study S- and T-dualities of these theories and argue the existence of a U-duality group.

scholarly journals STEPHEN HAWKING: SPACE, TIME AND QUANTA

2020 ◽  
Author(s):  
Mauro Carfora
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Space Time ◽  
Stephen Hawking

A brief introduction to the scientic work of Stephen Hawking and to his contributions to our understanding of the interplay between general relativity and quantum theory.

“Prehistoric” Quantum Gravity

2020 ◽  
pp. 41-70
Author(s):  
Dean Rickles
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Quantum Gravity ◽  
Philosophical Nature

In this chapter we examine the very earliest work on the problem of quantum gravity (understood very liberally). We show that, even before the concept of the quantization of the gravitational field in 1929, there was a fairly lively investigation of the relationships between gravity and quantum stretching as far back as 1916, and certainly no suggestion that such a theory would not be forthcoming. Indeed, there are, rather, many suggestions explicitly advocating that an integration of quantum theory and general relativity (or gravitation, at least) is essential for future physics, in order to construct a satisfactory foundation. We also see how this belief was guided by a diverse family of underlying agendas and constraints, often of a highly philosophical nature.

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