scholarly journals Little group generators for Dirac neutrino one-particle states

2021 ◽  
Vol 67 (1 Jan-Feb) ◽  
pp. 25
Author(s):  
R. Romero
Keyword(s):  
Hilbert Space ◽  
Field Operator ◽  
Charge Conjugation ◽  
Dirac Neutrino ◽  
Dirac Type ◽  
Massive Neutrinos ◽  
The One

Assuming neutrinos to be of the Dirac type, the little group generators for the one-particle states, created off the vacuum by the field operator, are obtained, both in terms of the one-particle states themselves and in terms of creation/annihilation operators. It is shown that these generators act also as rotation operators in the Hilbert space of the states, providing three types of transformations: a helicity flip, the standard charge conjugation, and a combination of the two, up to phases. The transformations’ properties are provided in detail and their physical implications discussed. It is also shown that one of the transformations continues to hold for chiral fields without mixing them. It is argued that these results provide support for the Majorana nature of massive neutrinos.

A quantization of the electromagnetic field

1983 ◽  
Vol 61 (8) ◽  
pp. 1172-1183
Author(s):  
Anton Z. Capri ◽  
Gebhard Grübl ◽  
Randy Kobes
Keyword(s):  
Hilbert Space ◽  
Electromagnetic Field ◽  
Gauge Invariance ◽  
Free Field ◽  
External Source ◽  
Field Level ◽  
Manifest Covariance ◽  
The One ◽  
Physical Spaces

Quantization of the electromagnetic field in a class of covariant gauges is performed on a positive metric Hilbert space. Although losing manifest covariance, we find at the free field level the existence of two physical spaces where Poincaré transformations are implemented unitarily. This gives rise to two different physical interpretations of the theory. Unitarity of the S operator for an interaction with an external source then forces one to postulate that a restricted gauge invariance must hold. This singles out one interpretation, the one where two transverse photons are physical.

scholarly journals QUANTIZATION OF THE G-CONNECTIONS VIA THE TANGENT GROUPOID

2013 ◽  
Vol 10 (09) ◽  
pp. 1320016
Author(s):  
ALAN LAI
Keyword(s):  
Hilbert Space ◽  
Convolution Operators ◽  
Gauge Action ◽  
Dirac Type

A description of the space of G-connections using the tangent groupoid is given. As the tangent groupoid parameter is away from zero, the G-connections act as convolution operators on a Hilbert space. The gauge action is examined in the tangent groupoid description of the G-connections. Tetrads are formulated as Dirac type operators. The connection variables and tetrad variables in Ashtekar's gravity are presented as operators on a Hilbert space.

scholarly journals The Modal-Hamiltonian Interpretation of Quantum Mechanics as a Kind of “Atomic” Interpretation

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Juan Sebastián Ardenghi ◽  
Olimpia Lombardi
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum State ◽  
The Other ◽  
Interpretation Of Quantum Mechanics ◽  
Modal Interpretation ◽  
Atomic Systems ◽  
Modal Interpretations ◽  
The One ◽  
The Relationship

Modal interpretations are non-collapse interpretations, where the quantum state of a system describes its possible properties rather than the properties that it actually possesses. Among them, the atomic modal interpretation (AMI) assumes the existence of a special set of disjoint systems that fixes the preferred factorization of the Hilbert space. The aim of this paper is to analyze the relationship between the AMI and our recently presented modal-hamiltonian interpretation (MHI), by showing that the MHI can be viewed as a kind of “atomic” interpretation in two different senses. On the one hand, the MHI provides a precise criterion for the preferred factorization of the Hilbert space into factors representing elemental systems. On the other hand, the MHI identifies the atomic systems that represent elemental particles on the basis of the Galilei group. Finally, we will show that the MHI also introduces a decomposition of the Hilbert space of any elemental system, which determines with precision what observables acquire definite actual values.

SELF-DUAL CONE ANALYSIS IN CONDENSED MATTER PHYSICS

2011 ◽  
Vol 23 (07) ◽  
pp. 749-822 ◽  
Author(s):  
TADAHIRO MIYAO
Keyword(s):  
Hilbert Space ◽  
Ground State ◽  
Condensed Matter ◽  
The Self ◽  
Physical Models ◽  
Condensed Matter Physics ◽  
Dual Cone ◽  
Operator Inequalities ◽  
The One ◽  
Phase Angles

The self-dual cone — the central object of this review — is introduced. Several operator inequalities associated with the self-dual cone are defined and mathematical properties of those are investigated. In general there are infinitely many choices of self-dual cones in a Hilbert space. Each of these lead to a distinct family of operator inequalities in the Hilbert space which enables us to analyze quantum physical models with respect to several aspects. We refer to these applications as self-dual cone analysis. The focus of this review lies on the self-dual cone analysis of models in condensed matter physics. In particular, by taking a physically proper self-dual cone, the interaction term of the Hamiltonian of the system becomes attractive from a viewpoint of our new operator inequalities. This attractive term enables us to analyze the system and various aspects of physical interest in detail. For instance, if the attractive term is ergodic, it is shown that the ground state is unique. By the uniqueness and the conservation laws, the physically symmetric state is realized as the ground state. This could be regarded as a physical order. As applications, the BCS model and the one-dimensional Fröhlich model are studied. We explain, from a viewpoint of the self-dual cone analysis, the appearance of macroscopic phase angles in the superconductors, Josephson effect and the Peierls instability.

scholarly journals A SIMPLE PROOF OF THE FUNDAMENTAL THEOREM ABOUT ARVESON SYSTEMS

2006 ◽  
Vol 09 (02) ◽  
pp. 305-314 ◽  
Author(s):  
MICHAEL SKEIDE
Keyword(s):  
Hilbert Space ◽  
Simple Proof ◽  
Fundamental Theorem ◽  
Hilbert Module ◽  
Bounded Operators ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Product Systems ◽  
Dimensional Hilbert Space ◽  
The One

With every E0-semigroup (acting on the algebra of of bounded operators on a separable infinite-dimensional Hilbert space) there is an associated Arveson system. One of the most important results about Arveson systems is that every Arveson system is the one associated with an E0-semigroup. In these notes we give a new proof of this result that is considerably simpler than the existing ones and allows for a generalization to product systems of Hilbert module (to be published elsewhere).

scholarly journals Latent Complete-Lattice Structure of Hilbert-Space Projectors

Quanta ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Fedor Herbut
Keyword(s):  
Hilbert Space ◽  
Complete Lattice ◽  
Lattice Structure ◽  
Infinite Dimensional ◽  
Mechanical Formalism ◽  
Quantum Mechanical Formalism ◽  
The One ◽  
Infinite Sums ◽  
Adjoint Operators ◽  
Countably Infinite

To uncover the hidden complete-lattice structure of Hilbert-space projectors, which is not seen by the operator operations and relations (algebraically), resort is taken to the ranges of projectors (to subspaces—to geometry). Taking the range of a projector is completed into a bijection of all projectors onto all subspaces of any finite or countably infinite dimensional Hilbert space. As a second step, this basic bijection is upgraded into an isomorphism of partially ordered sets utilizing the sub-projector relation on the one hand, and the subspace relation on the other. As a third and final step, the basic bijection is further upgraded to isomorphism of complete lattices. The complete-lattice structure is derived for subspaces, then, using the basic bijection, it is transferred to the set of all projectors. Some consequences in the quantum-mechanical  formalism are examined with particular attention to the infinite sums appearing in spectral decompositions of discrete self-adjoint operators with infinite spectra.Quanta 2019; 8: 1–10.

scholarly journals A Formal Model of Metaphor in Frame Semantics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Hilbert Space ◽  
Wave Function ◽  
Formal Model ◽  
Quantum Computer ◽  
Formal Semantics ◽  
Formal Definition ◽  
Frame Semantics ◽  
The One ◽  
Definition Of ◽  
The Mathematical Model

A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a wave function in Hilbert space. The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered. A series of formal definitions is deduced from this for: “representation”, “reality”, “language”, “ontology”, etc. All are based on Hilbert space. A few statements about a quantum computer are implied: The so-defined reality is inherent and internal to it. It can report a result only “metaphorically”. It will demolish transmitting the result “literally”, i.e. absolutely exactly. A new and different formal definition of metaphor is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above. The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought. Four areas of cognition are unified as different but isomorphic interpretations of the mathematical model based on Hilbert space. These are: quantum mechanics, frame semantics, formal semantics by means of quantum computer, and the theory of metaphor in linguistics.

scholarly journals Locality and General Vacua in Quantum Field Theory

2021 ◽  
Author(s):  
Daniele Colosi ◽  
◽  
Robert Oeckl ◽  
◽  
◽  
...  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Vacuum State ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Algebraic Quantum ◽  
Particle Pairs ◽  
The One ◽  
Gns Construction

We extend the framework of general boundary quantum field theory (GBQFT) to achieve a fully local description of realistic quantum field theories. This requires the quantization of non-Kähler polarizations which occur generically on timelike hypersurfaces in Lorentzian spacetimes as has been shown recently. We achieve this in two ways: On the one hand we replace Hilbert space states by observables localized on hypersurfaces, in the spirit of algebraic quantum field theory. On the other hand we apply the GNS construction to twisted star-structures to obtain Hilbert spaces, motivated by the notion of reflection positivity of the Euclidean approach to quantum field theory. As one consequence, the well-known representation of a vacuum state in terms of a sea of particle pairs in the Hilbert space of another vacuum admits a vast generalization to non-Kähler vacua, particularly relevant on timelike hypersurfaces.

scholarly journals Clustering in massive neutrino cosmologies via Eulerian Perturbation Theory

2021 ◽  
Vol 2021 (11) ◽  
pp. 028
Author(s):  
Alejandro Aviles ◽  
Arka Banerjee ◽  
Gustavo Niz ◽  
Zachary Slepian
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Effective Field ◽  
Tree Level ◽  
Accurate Approximation ◽  
Bias Parameter ◽  
Wave Numbers ◽  
Massive Neutrinos ◽  
Correct Estimation ◽  
The One

Abstract We introduce an Eulerian Perturbation Theory to study the clustering of tracers for cosmologies in the presence of massive neutrinos. Our approach is based on mapping recently-obtained Lagrangian Perturbation Theory results to the Eulerian framework. We add Effective Field Theory counterterms, IR-resummations and a biasing scheme to compute the one-loop redshift-space power spectrum. To assess our predictions, we compare the power spectrum multipoles against synthetic halo catalogues from the QUIJOTE simulations, finding excellent agreement on scales k ≲ 0.25 h Mpc-1. One can obtain the same fitting accuracy using higher wave-numbers, but then the theory fails to give a correct estimation of the linear bias parameter. We further discuss the implications for the tree-level bispectrum. Finally, calculating loop corrections is computationally costly, hence we derive an accurate approximation wherein we retain only the main features of the kernels, as produced by changes to the growth rate. As a result, we show how FFTLog methods can be used to further accelerate the loop computations with these reduced kernels.

scholarly journals Two conditions for subnormality of unbounded operators

2001 ◽  
Vol 43 (1) ◽  
pp. 23-28
Author(s):  
Jan Niechwiej
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Bounded Operators ◽  
Unbounded Operators ◽  
The Real ◽  
Completely Monotonic ◽  
Binomial Expansion ◽  
Hilbert Space Operators ◽  
The One

We give two new sufficient conditions for unbounded Hilbert space operators to be subnormal. The first assumes that the sequence //Tnf//2 on a suitable subset of the domain is completely monotonic, the second is similar to the one given by Lambert in [3] for bounded operators and involves the sequence of binomial expansion of the real part of the operator.

Sign in / Sign up

Export Citation Format

Share Document