scholarly journals Conserved Quantities of Field Theory on Discrete Spacetime

1995 ◽  
Vol 93 (1) ◽  
pp. 173-184 ◽  
Author(s):  
H. Yamamoto ◽  
A. Hayashi ◽  
T. Hashimoto ◽  
M. Horibe
Keyword(s):  
Field Theory ◽  
Conserved Quantities ◽  
Discrete Spacetime

ATTEMPTS TO DEFINE QUASI-INTEGRABILITY

2012 ◽  
Vol 09 (06) ◽  
pp. 1261004 ◽  
Author(s):  
LUIZ A. FERREIRA ◽  
WOJTEK J. ZAKRZEWSKI
Keyword(s):  
Field Theory ◽  
Integrable Systems ◽  
Integrable Model ◽  
Conserved Quantities ◽  
Preliminary Results ◽  
Sine Gordon Model

In this paper we discuss some ideas on how to define the concept of quasi-integrability. Our ideas stem from the observation that many field theory models are "almost" integrable; i.e. they possess a large number of "almost" conserved quantities. Most of our discussion will involve a certain class of models which generalize the sine-Gordon model in (1 + 1) dimensions. As will be mentioned many field configurations of these models look like those of the integrable systems and so appear to be close to those in integrable model. We will then attempt to quantify these claims looking in particular, both analytically and numerically, at field configurations with scattering solitons. We will also discuss some preliminary results obtained in other models.

scholarly journals Emerging Quantum Fields Embedded in the Emergence of Spacetime

2018 ◽  
Author(s):  
Hans Diel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Causal Model ◽  
Space Time ◽  
Quantum Field ◽  
Quantum Fields ◽  
Standard Quantum ◽  
Discrete Spacetime ◽  
Feynman Rules ◽  
Space Point

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. At the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighbor space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points.  Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques  (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to  n > 3  in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

scholarly journals Emerging Quantum Fields Embedded in the Emergence of Spacetime

2018 ◽  
Author(s):  
Hans Diel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Causal Model ◽  
Space Time ◽  
Quantum Field ◽  
Quantum Fields ◽  
Standard Quantum ◽  
Discrete Spacetime ◽  
Feynman Rules ◽  
Space Point

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. On the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighboring space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points. Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to n > 3 in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

scholarly journals Emerging Quantum Fields Embedded in the Emergence of Spacetime

2018 ◽  
Author(s):  
Hans Diel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Causal Model ◽  
Space Time ◽  
Quantum Field ◽  
Quantum Fields ◽  
Standard Quantum ◽  
Discrete Spacetime ◽  
Feynman Rules ◽  
Space Point

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. At the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighbor space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points. Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to n > 3 in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

scholarly journals A Model of Spacetime Dynamics with Embedded Quantum Objects

2017 ◽  
Vol 01 (03) ◽  
pp. 1750010
Author(s):  
Hans H. Diel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Building Blocks ◽  
Relativity Theory ◽  
Quantum Field ◽  
Dynamical Object ◽  
Discrete Spacetime ◽  
Proposed Model ◽  
Quantum Objects ◽  
Physical Objects

General relativity theory (GRT) tells us that (a) space and time should be viewed as an entity (called spacetime), (b) the spacetime of a world that contains gravitational objects should be viewed as curved, and (c) spacetime is a dynamical object with a dynamically changing extent and curvature. Attempts to achieve compatibility of GRT with quantum theory (QT) have typically resulted in proposing elementary units of spacetime as building blocks for the emergence of larger spacetime objects. In the present paper, a model of curved discrete spacetime is presented in which the basic space elements are derived from Causal Dynamical Triangulation. Spacetime can be viewed as the container for physical objects, and in GRT, the energy distribution of the contained physical objects determines the dynamics of spacetime. In the proposed model of curved discrete spacetime, the primary objects contained in spacetime are “quantum objects”. Other larger objects are collections of quantum objects. This approach results in an accordance of GRT and quantum (field) theory, while coincidently the areas in which their laws are in force are separated. In the second part of the paper, a rough mapping of quantum field theory to the proposed model of spacetime dynamics is described.

scholarly journals AUGMENTED VARIATIONAL PRINCIPLES AND RELATIVE CONSERVATION LAWS IN CLASSICAL FIELD THEORY

2005 ◽  
Vol 02 (03) ◽  
pp. 373-392 ◽  
Author(s):  
L. FATIBENE ◽  
M. FERRARIS ◽  
M. FRANCAVIGLIA
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Variational Principles ◽  
Classical Mechanics ◽  
Classical Field Theory ◽  
Conserved Quantities ◽  
Fundamental Physics ◽  
Relative Conservation ◽  
Formal Integration ◽  
Definition Of

Augmented variational principles are introduced in order to provide a definition of relative conservation laws. As it is physically reasonable, relative conservation laws define in turn relative conserved quantities that measure, for example, how much energy is needed in a field theory to go from one configuration (called the reference or vacuum) to another configuration (the physical state of the system). The general prescription we describe solves in a covariant way the well-known observer dependence of conserved quantities. The solution found is deeply related to the divergence ambiguity of the Lagrangian and to various formalisms that have recently appeared in literature to deal with the variation of conserved quantities (of which this is a formal integration). A number of examples relevant to fundamental physics are considered in detail, starting from classical mechanics.

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