Related papers: "Fields" in classical and quantum field theories
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics…
Following the spirit of de Broglie and Einstein, we think the concepts of matter and radiation can be unified. We know a particle propagates like a wave; its motion is described by certain wave equations. At this point, it is not clear what…
The framework of locally covariant quantum field theory is discussed, motivated in part using "ignorance principles". It is shown how theories can be represented by suitable functors, so that physical equivalence of theories may be…
We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that…
Since the early days of search for a quantum theory of gravity the attempts have been mostly concentrated on the quantization of an otherwise classical system. The two most contentious candidate theories of gravity, sting theory and quantum…
If the systems of quantum theory are thought of as elementary information carriers in the first place, rather than elementary constituents of matter, and their connections are logical connections within a given algorithm, rather than…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in…
Quantum field theory (QFT) based on the principles of special relativity (SR) and it is in fact the \emph{kinematic theory of fields}. The root assumption is that there is "relativistic description" of \emph{any} isolated quantum system in…
We explore finite-field frameworks for quantum theory and quantum computation. The simplest theory, defined over unrestricted finite fields, is unnaturally strong. A second framework employs only finite fields with no solution to x^2+1=0,…
We consider the quantum Hall effect in terms of an effective field theory formulation of the edge states, providing a natural common framework for the fractional and integral effects.
This elementary introduction to string field theory highlights the features and the limitations of this approach to quantum gravity as it is currently understood. String field theory is a formulation of string theory as a field theory in…
We offer a perspective on some recent results obtained in the context of the group field theory approach to quantum gravity, on top of reviewing them briefly. These concern a natural mechanism for the emergence of non-commutative field…
Quantum field theory unifies concepts from quantum theory and from special relativity. Its mathematically rigorous description is quite intricate and is only partially understood; this is particularly true for the construction of operators…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…
We argue that the conventional quantum field theory in curved spacetime has a grave drawback: The canonical commutation relations for quantum fields and conjugate momenta do not hold. Thus the conventional theory should be denounced and the…
Any acceptable quantum gravity theory must allow us to recover the classical spacetime in the appropriate limit. Moreover, the spacetime geometrical notions should be intrinsically tied to the behavior of the matter that probes them. We…
We explore a field theoretical approach to quantum computing and control. This book consists of three parts. The basics of systems theory and field theory are reviewed in Part I. In Part II, a gauge theory is reinterpreted from a systems…
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…