scholarly journals Mixed Models: Combining incompatible scalar models in any space–time dimension

2017 ◽  
Vol 32 (01) ◽  
pp. 1750001
Author(s):  
John R. Klauder
Keyword(s):  
Quantum Theory ◽  
Mixed Models ◽  
Specific Interaction ◽  
Free Action ◽  
General Rule ◽  
Space Time ◽  
Time Dimension ◽  
Classical Action ◽  
Dimension Formula ◽  
Special Cases

Traditionally, covariant scalar field theory models are either super renormalizable, strictly renormalizable, or nonrenormalizable. The goal of “Mixed Models” is to make sense of sums of these distinct examples, e.g. [Formula: see text], which includes an example of each kind for space–time dimension [Formula: see text]. We show how the several interactions such mixed models have may be turned on and off in any order without any difficulties. Analogous results are shown for [Formula: see text], etc. for all [Formula: see text]. Different categories hold for [Formula: see text] such as, e.g. [Formula: see text], that involve polynomial [Formula: see text] and suitable nonpolynomial [Formula: see text] interactions, etc. Analogous situations for [Formula: see text] (time alone) offer simple “toy” examples of how such mixed models may be constructed. As a general rule, if the introduction of a specific interaction term reduces the domain of the free classical action, we invariably find that the introduction of the associated quantum interaction leads, effectively, to a “nonrenormalizable” quantum theory. However, in special cases, a classical interaction that does not reduce the domain of the classical free action may generate an “unsatisfactory” quantum theory, which generally involves a model-specific, different approach to become “satisfactory.” We will encounter both situations in our analysis.

scholarly journals THE ORBIFOLD-STRING THEORIES OF PERMUTATION-TYPE II: CYCLE DYNAMICS AND TARGET SPACE–TIME DIMENSIONS

2010 ◽  
Vol 25 (30) ◽  
pp. 5487-5515
Author(s):  
M. B. HALPERN
Keyword(s):  
Physical State ◽  
Central Charge ◽  
Space Time ◽  
Target Space ◽  
Twisted Sector ◽  
Time Dimension ◽  
State Problem ◽  
Dimension Formula ◽  
Charge Formula ◽  
String Theories

We continue our discussion of the general bosonic prototype of the new orbifold-string theories of permutation-type. Supplementing the extended physical-state conditions of the previous paper, we construct here the extended Virasoro generators with cycle central charge [Formula: see text], where fj(σ) is the length of cycle j in twisted sector σ. We also find an equivalent, reduced formulation of each physical-state problem at reduced cycle central charge cj(σ) = 26. These tools are used to begin the study of the target space–time dimension [Formula: see text] of cycle j in sector σ, which is naturally defined as the number of zero modes (momenta) of each cycle. The general model-dependent formulae derived here will be used extensively in succeeding papers, but are evaluated in this paper only for the simplest case of the "pure" permutation orbifolds.

scholarly journals THE ORBIFOLD-STRING THEORIES OF PERMUTATION-TYPE III: LORENTZIAN AND EUCLIDEAN SPACE—TIMES IN A LARGE EXAMPLE

2011 ◽  
Vol 26 (13) ◽  
pp. 2199-2231
Author(s):  
M. B. HALPERN
Keyword(s):  
Space Time ◽  
Target Space ◽  
Permutation Groups ◽  
Twisted Sector ◽  
Time Dimension ◽  
Dimension Formula ◽  
Time Symmetry ◽  
Time Signature ◽  
The Many ◽  
String Theories

To illustrate the general results of the previous paper, we discuss here a large concrete example of the orbifold-string theories of permutation-type. For each of the many subexamples, we focus on evaluation of the target space–time dimension[Formula: see text], the target space–time signature and the target space–time symmetry of each cycle j in each twisted sector σ. We find in particular a gratifying space–time symmetry enhancement which naturally matches the space–time symmetry of each cycle to its space–time dimension. Although the orbifolds of ℤ2-permutation-type are naturally Lorentzian, we find that the target space–times associated with larger permutation groups can be Lorentzian, Euclidean and even null [Formula: see text], with varying space–time dimensions, signature and symmetry in a single orbifold.

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.

scholarly journals GENERALIZED W3-STRINGS FROM FREE FIELDS

1995 ◽  
Vol 10 (06) ◽  
pp. 515-524 ◽  
Author(s):  
J. M. FIGUEROA-O'FARRILL ◽  
C. M. HULL ◽  
L. PALACIOS ◽  
E. RAMOS
Keyword(s):  
Bosonic Strings ◽  
Free Field ◽  
Space Time ◽  
General Construction ◽  
Special Cases ◽  
Free Fields ◽  
Rule Out ◽  
General Conditions ◽  
String Theories

The conventional quantization of w3-strings gives theories which are equivalent to special cases of bosonic strings. We explore whether a more general quantization can lead to new generalized W3-string theories by seeking to construct quantum BRST charges directly without requiring the existence of a quantum W3-algebra. We study W3-like strings with a direct space-time interpretation — that is, with matter given by explicit free field realizations. Special emphasis is placed on the attempt to construct a quantum W-string associated with the magic realizations of the classical w3-algebra. We give the general conditions for the existence of W3-like strings, and comment on how the known results fit into our general construction. Our results are negative: we find no new consistent string theories, and in particular rule out the possibility of critical strings based on the magic realizations.

scholarly journals Relativity and the quantum theory

1928 ◽  
Vol 117 (778) ◽  
pp. 630-637 ◽  
Keyword(s):  
Quantum Theory ◽  
Space Time ◽  
Theory Of Gravitation ◽  
The Law

In Einstein’s theory of gravitation it is assumed that the geometry of space- time is characterised by the following equation for the measurement of displacement:— ds 2 = g mn dx m dx n { m n = 1, 2, 3, 4, the sign of summation being omitted for convenience. It is supposed that the coefficients, of which g mn is the type, are dependent upon the content of space, and the relation existing between them is the law of gravitation.

scholarly journals POLYHOMOGENEOUS SOLUTIONS OF NONLINEAR WAVE EQUATIONS WITHOUT CORNER CONDITIONS

2006 ◽  
Vol 03 (01) ◽  
pp. 81-141 ◽  
Author(s):  
PIOTR T. CHRUŚCIEL ◽  
SZYMON ŁȨSKI
Keyword(s):  
Initial Data ◽  
Wave Equations ◽  
Space Time ◽  
Einstein Equations ◽  
Nonlinear Wave Equations ◽  
Linear Wave ◽  
Cauchy Problems ◽  
Time Dimension ◽  
Wave Maps ◽  
Corner Conditions

The study of Einstein equations leads naturally to Cauchy problems with initial data on hypersurfaces which closely resemble hyperboloids in Minkowski space-time, and with initial data with polyhomogeneous asymptotics, that is, with asymptotic expansions in terms of powers of ln r and inverse powers of r. Such expansions also arise in the conformal method for analysing wave equations in odd space-time dimension. In recent work it has been shown that for non-linear wave equations, or for wave maps, polyhomogeneous initial data lead to solutions which are also polyhomogeneous provided that an infinite hierarchy of corner conditions holds. In this paper we show that the result is true regardless of corner conditions.

Negative admissibility of evidence in public law litigation: reflections on the exercise of public authorities’ power in relation to the proof process

2021 ◽  
pp. 800-808
Author(s):  
Dmitry B. Abushenko
Keyword(s):  
General Rule ◽  
Court Case ◽  
Court Cases ◽  
Public Authorities ◽  
Judicial Practice ◽  
General Logic ◽  
Special Cases ◽  
The Status ◽  
Judicial Procedure ◽  
Public Law Litigation

We consider the issues of the implementation of certain public authorities in relation to a future judicial dispute. We define the boundaries of use of additional evidentiary tools through the prism of the powers vested in other (non-parties in a particular court case) public entities. We substantiate the applicability of the general rule on negative admissibility, we highlight special cases when evidence previously obtained by an authority that does not have the status of a person participating in the case could still be submitted to a court case initiated on a dispute involving a public authority. The general logic of the proposed approach can be applied both to a procedural private opponent when he received “reinforcement” due to the actions of another authority, and can also be used for private law disputes. We conclude that the absence in the current Russian legislation of any norms that build in-tersectoral relations with regard to the institution of negative admissibility of evidence obtained by other authorities not only generates contradictions in judicial practice, but also in a certain sense discredits the adversarial judicial procedure itself and discourages public authorities, which begin to operate with special tools to combat socially dangerous acts in “ordinary” court cases.

scholarly journals NEW SUPERSTRING ISOMETRIES AND HIDDEN DIMENSIONS

2007 ◽  
Vol 22 (29) ◽  
pp. 5301-5323 ◽  
Author(s):  
DIMITRI POLYAKOV
Keyword(s):  
Extra Dimension ◽  
Isometry Group ◽  
Space Time ◽  
Time Dimension ◽  
Superstring Theory ◽  
Symmetry Transformations ◽  
Noncritical Strings ◽  
A Chain ◽  
Symmetry Generators ◽  
Special Space

We study the hierarchy of hidden space–time symmetries of noncritical strings in RNS formalism, realized nonlinearly. Under these symmetry transformations the variation of the matter part of the RNS action is canceled by that of the ghost part. These symmetries, referred to as the α-symmetries, are induced by special space–time generators, violating the equivalence of ghost pictures. We classify the α-symmetry generators in terms of superconformal ghost cohomologies Hn ~ H-n-2(n≥0) and associate these generators with a chain of hidden space–time dimensions, with each ghost cohomology Hn ~ H-n-2 "contributing" an extra dimension. Namely, we show that each ghost cohomology Hn ~ H-n-2 of noncritical superstring theory in d-dimensions contains d+n+1 α-symmetry generators and the generators from Hk ~ H-k-2, 1≤k ≤n, combined together, extend the space–time isometry group from the naive SO (d, 2) to SO (d+n, 2). In the simplest case of n = 1 the α-generators are identified with the extra symmetries of the 2T-physics formalism, also known to originate from a hidden space–time dimension.

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.

scholarly journals A Critical Review of Works Pertinent to the Einstein-Bohr Debate and Bell’s Theorem

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 163
Author(s):  
Karl Hess
Keyword(s):  
Quantum Theory ◽  
Physical Reality ◽  
Point Of View ◽  
Statistical Sampling ◽  
Necessary And Sufficient Condition ◽  
Special Cases ◽  
General Physical ◽  
Necessary And Sufficient ◽  
Physical Features ◽  
Chsh Inequalities

This review is related to the Einstein-Bohr debate and to Einstein–Podolsky–Rosen’s (EPR) and Bohm’s (EPRB) Gedanken-experiments as well as their realization in actual experiments. I examine a significant number of papers, from my minority point of view and conclude that the well-known theorems of Bell and Clauser, Horne, Shimony and Holt (CHSH) deal with mathematical abstractions that have only a tenuous relation to quantum theory and the actual EPRB experiments. It is also shown that, therefore, Bell-CHSH cannot be used to assess the nature of quantum entanglement, nor can physical features of entanglement be used to prove Bell-CHSH. Their proofs are, among other factors, based on a statistical sampling argument that is invalid for general physical entities and processes and only applicable for finite “populations”; not for elements of physical reality that are linked, for example, to a time-like continuum. Bell-CHSH have, furthermore, neglected the subtleties of the theorem of Vorob’ev that includes their theorems as special cases. Vorob’ev found that certain combinatorial-topological cyclicities of classical random variables form a necessary and sufficient condition for the constraints that are now known as Bell-CHSH inequalities. These constraints, however, must not be linked to the observables of quantum theory nor to the actual EPRB experiments for a variety of reasons, including the existence of continuum-related variables and appropriate considerations of symmetry.

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