When incorporating the GUP into quantum field theory
, as mentioned in the Introduction, there are two kinds of realizations, one of which respects covariance and the other does not.
Our brief exposition for the description of these large systems will be done within the framework set by the connection of Wightman quantum field theory
(see [49, 50]) with the theory of local nets of C' or von Neumann algebras ([5, 51], see also ; for all details, see ).
The universe described by quantum field theory
is subject to the stringent constraint of a certain rule-set, or symmetry, known as Lorentz symmetry, which is characteristic of high-energy particles.
Its purpose is to elucidate an explanation of why quantum field theory
works and give a framework for modifications, like the inclusion of gravity, that may have a well posed structure but not exist in the framework of QFT itself.
The matter that creates the spacetime curvature, however, is treated using quantum field theory
. The resulting theory cannot be ultimately acceptable because it mixes classical and quantum physics, but it should be a valuable tool and an approximate description of the behavior of nature over length scales (and energy scales) that reach down towards the realm where string theory may provide an ultimate exegesis.
On the other hand, it can happen that one has reason to believe that there are many acceptable quantizations of the system (each appropriate for modelling a distinct physical situation), or that the structure of the classical system does not single out a preferred quantization (as in quantum field theory
on curved spacetime).
By applying general relativity and quantum field theory
on curved spacetime, Hawking arrives at the conclusion that the information is lost in the black holes, and this breaks the predictability .
The accuracy of QM and its modern version, quantum field theory
, is so great that no one who is serious enough can question QM.
The popularity of "continuous field" based GR have been responsible for the undermining of the original particle based orientation of quantum electrodynamics (QED); as "field" based theories like quantum field theory
(QFT) now dominate quantum mechanics and the related domains of cosmology.
(51) The Standard Model is a quantum theory, more properly, a quantum field theory
that regards point-like particles as quantum excitations of fields; the photon, for example, may be treated as a quantized excitation of electromagnetic field, or more simply, a tiny bundle of light.
In a revision and English translation of the 2003 Russian edition of a book based on the extended lecture course he has taught since 1991, he sets out the fundamentals for graduate students and young researchers who are working mainly in condensed matter physics, emphasizing the links between quantum field theory
and modern condensed matter theory.
The first six chapters are detailed expositions of the Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion category theory, topological quantum field theory
, and anyon theory.
Inflation, Steinhardt says, is based on quantum field theory
, which views every elementary particle as a point-like object.
The mechanism of SBS was first demonstrated theoretically in quantum field theory
: (1) In the system of infinitely many degrees of freedom described by the Hamiltonian manifesting the rotational symmetry, only one state is chosen spontaneously among the infinitely degenerate ground states as a real ground state of the system and the rotational symmetry of the system is broken without recourse to any external environment.
This book provides a sustained attempt to give an interpretation of quantum field theory
along broadly Kantian lines.