Bound State Description of Particles from a Quantum Field Theory of Fermions and Bosons, Compatible with Relativity

Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix elements from a dual fermion-boson Lagrangian. In this formalism, the fermion binding energies are compensated by boson energies, indicating that particles can be generated out of the vacuum. This yields quantitative solutions for various mesons ω (0.78 GeV) - Υ (9.46 GeV) and all leptons e, μ and τ, with uncertainties in the extracted properties of less than 1‰. For transparency, a Web-page with the address htpps://h2909473.stratoserver.net has been constructed, where all calculations can be run on line and also the underlying fortran source code can be inspected.

GENERALIZED OPERATORS AND OPERATOR-VALUED DISTRIBUTIONS IN QUANTUM FIELD THEORY

The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.

TOPOLOGICAL STRUCTURE OF RENORM ALIZATION CONSTANTS I N QUANTUM FIELD THEORY AT SHORT DISTANCE KUNMING COLLABRATION OF MULTIHADRON DYNAMIOS

The anomalous dimensions of the quantum fields are the Hausdorff dimensiongrad. The present candidate of the renormalization constant is the generalized Cantor discontinuum. The Hausdorff dimensiongrad of the Minkowski space time is based upon the point set with σ-length on light cone.

GENERALIZED OPERATORS AND P(φ)_2 QUANTUM FIELDS

In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation of renormalization procedure is given under white noise theory.

Evidence for Expanding Quantum Field Theory

Present day Quantum Field Theory (QFT) is founded on canonical quantization, which has served quite well but also has led to several issues. The free field describing a free particle (with no interaction term) can suddenly become nonrenormalizable the instant a suitable interaction term appears. For example, using canonical quantization , has been deemed a “free” theory with no difference from a truly free field [1] [2]. Using the same model, affine quantization has led to a truly interacting theory [3]. This fact alone asserts that canonical and affine tools of quantization deserve to be open to their procedures together as a significant enlargement of QFT.

Higher-order squeezing of quantum field and higher-order uncertainty relations in non-degenerate four-wave mixing

It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the hlgher-order uncertainty relations in the process of non-degenerate four-wave mixing are presented for the first time. The product of higher-order noise moments is related to even order number N and the length L of the medium.

Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters

This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters.The boson-fermion correspondence for these symmetric functions have been presented.In virtue of quantum fields,we derive a series of infinite order nonlinear integrable equations,namely,universal character hierarchy,symplectic KP hierarchy and symplectic universal character hierarchy,respectively.In addition,the solutions of these integrable systems have been discussed.

Quantum Field Theory Deserves Extra Help

Today's quantum field theory (QFT) relies heavenly on canonical quantization (CQ), which fails for φ44 leading only to a “free” result. Affine quantization (AQ), an alternative quantization procedure, leads to a “non-free” result for the same model. Perhaps adding AQ to CQ can improve the quantization of a wide class of problems in QFT.

Cosmic Dark Energy from ‘t Hooft’s Dimensional Regularization and Witten’s Topological Quantum Field Pure Gravity

We utilize two different theories to prove that cosmic dark energy density is the complimentary Legendre transformation of ordinary energy and vice versa as given by E(dark) = mc2 (21/22) and E(ordinary) = mc2/22. The first theory used is based on G ‘t Hooft’s remarkably simple renormalization procedure in which a neat mathematical maneuver is introduced via the dimensionality of our four dimensional spacetime. Thus, ‘t Hooft used instead of D = 4 and then took at the end of an intricate and subtle computation the limit to obtain the result while avoiding various problems including the pole singularity at D = 4. Here and in contradistinction to the classical form of dimensional and renormalization we set and do not take the limit where and is the theoretically and experimentally well established Hardy’s generic quantum entanglement. At the end we see that the dark energy density is simply the ratio of and the smooth disentangled D = 4, i.e. (dark) = (4 -k)/4 = 3.8196011/4 = 0.9549150275. Consequently where we have ignored the fine structure details by rounding 21 + k to 21 and 22 + k to 22 in a manner not that much different from of the original form of dimensional regularization theory. The result is subsequently validated by another equally ingenious approach due mainly to E. Witten and his school of topological quantum field theory. We notice that in that theory the local degrees of freedom are zero. Therefore, we are dealing essentially with pure gravity where are the degrees of freedom and is the corresponding dimension. The results and the conclusion of the paper are summarized in Figure 1-3, Table 1 and Flow Chart 1.

Classical Quantum Field Theory Based on the Hypothesis of the Absolute Reference System

The quantum field theory based on the hypothesis of the absolute reference system is a classical non-relativistic theory, which is compatible with current quantum theory. This conclusion arises when one compares the theoretical results of quantum electrodynamics using the basic principles of this hypothesis. Wave equation, which replaces this of Schrodinger, is the classical wave equation of a peculiar electromagnetic wave, derived from the study of particle structure.

Guidelines to Quantum Field Interactions in Vacuum

In this treatise we stress the analogy between strongly interacting many-body systems and elementary particle physics in the context of Quantum Field Theory (QFT). The common denominator between these two branches of theoretical physics is the Green’s function or propagator, which is the key for solving specific problems. Here we are concentrating on the vacuum, its excitations and its interaction with electron and photon fields.

A Quantum Field Theory Toy-Model for Magnetic Epigenetic

We consider the effects that a magnetic field has on the observable properties of an elementary one-fermion state, assumed for simplicity to be that of one electron. We show that for a weak intensity of the field these effects can be very simply computed in a quantum field theory theoretical framework, assuming the minimal form of the electromagnetic interaction and the validity of the Dirac equation. The effects proceed via preliminary, magnetic field induced, modification of the four components of the spinor field. These generate consequent modifications of the various observable properties of the fermion, which can always be simply expressed in terms of the four spinor field components. A few general features of the various effects are discussed, and a number of possible analogies with the fascinating medical description of the epigenetic process for an organic cell are finally proposed.

Combined Environmental and Magnetic Effects on Elementary Matter: A Quantum Field Theory Description of Fermion Epigenetics

We compute in a theoretical quantum field theory framework the effects that a classic environment will have on an elementary one-fermion state, assumed for simplicity to be that of one electron, in the presence of a magnetic field. We consider its total energy and its spin angular momentum as relevant observables of the state. We show that the changes of these quantities produced by the combined environmental and magnetic effects can be expressed in a simple and compact form. We obtain expressions that only depend on the values of the external environment and magnetic fields, and on the special spin features of the free fermion state. We call these effects “fermion epigenetics” and try to motivate this definition discussing possible relevant analogies with the corresponding medical treatment of epigenetics in organic cells.

Holographic Bound in Quantum Field Energy Density and Cosmological Constant

The cosmological constant problem is reanalyzed by imposing the limitation of the number of degrees of freedom (d.o.f.) due to entropy bounds directly in the calculation of the energy density of a field theory. It is shown that if a quantum field theory has to be consistent with gravity and holography, i.e. with an upper limit of storing information in a given area, the ultraviolet momentum cut-off is not the Planck mass, Mp, as naively expected, but where Nu is the number of d.o.f. of the universe. The energy density evaluation turns out completely consistent with Bousso’s bound on the cosmological constant value. The scale , that in the “fat graviton” theory corresponds to the graviton size, originates by a self-similar rearrangement of the elementary d.o.f. at different scales that can be seen as an infrared-ultraviolet connection.

Generalization via Ultrahyperfunctions of a Gupta-Feynman Based Quantum Field Theory of Einstein’s Gravity

Ultrahyperfunctions (UHF) are the generalization and extension to the complex plane of Schwartz’ tempered distributions. This effort is an application to Einstein’s gravity (EG) of the mathematical theory of convolution of Ultrahyperfunctions developed by Bollini et al. [1] [2] [3] [4]. A simplified version of these results was given in [5] and, based on them;a Quantum Field Theory (QFT) of EG [6] was obtained. Any kind of infinities is avoided by recourse to UHF. We will quantize EG by appealing to the most general quantization approach, the Schwinger-Feynman variational principle, which is more appropriate and rigorous that the popular functional integral method (FIM). FIM is not applicable here because our Lagrangian contains derivative couplings. We follow works by Suraj N. Gupta and Richard P. Feynman so as to undertake the construction of an EG-QFT. We explicitly use the Einstein Lagrangian as elaborated by Gupta [7], but choose a new constraint for the ensuing theory. In this way, we avoid the problem of lack of unitarity for the S matrix that afflicts the procedures of Gupta and Feynman. Simultaneously, we significantly simplify the handling of constraints, which eliminates the need to appeal to ghosts for guarantying unitarity of the theory. Our approach is obviously non-renormalizable. However, this inconvenience can be overcome by appealing to the mathematical theory developed by Bollini et al. [1] [2] [3] [4] [5]. Such developments were founded in the works of Alexander Grothendieck [8] and in the theory of Ultradistributions of Jose Sebastiao e Silva [9] (also known as Ultrahyperfunctions). Based on these works, an edifice has been constructed along two decades that are able to quantize non-renormalizable Field Theories (FT). Here we specialize this mathematical theory to discuss EG-QFT. Because we are using a Gupta-Feynman inspired EG Lagrangian, we are able to evade the intricacies of Yang-Mills theories.

Reformulation of Relativistic Quantum Field Theory Using Region-Like Idealization of the Elementary Particle

The existence of any elementary particle in universe requires the existence of some region of universe occupied by it. By taking the volume of this occupied region, the author will reformulate the relativistic quantum field theory using new 3-dimensional region-like idealization of elementary particles and hereinafter will call the total volume of all regions occupied by the elementary constituent particles of the quantum system the occupied volume. Also the author will call the set of all regions of universe filled by elementary constituent particles of the quantum system the occupied path. Always any quantum system is existed at a head of its occupied path. This path is growing by mutual filling and leaving regions of universe by its elementary constituent particles. The conservation of this elementary constituent particle requires the conservation of its occupied volume during this process. This requirement could be summarized by the following conditions: 1) the total volume of all regions of universe filled by the elementary constituent particles of the quantum system minus the total volume of all regions of universe left by these elementary constituent particles must be equal to the occupied volume of the quantum system;2) the total increase in the occupied volume of the quantum system due to the absorption of another elementary particles from outside its occupied regions minus the total decreasing in its occupied volume due to the emission of another elementary particles outside its occupied regions must be equal to the occupied volume of it. The wave-particle duality of the elementary constituent particles implied accumulation of them as the finite set of interfered waves. This accumulation of elementary constituent particles causes the absolute probabilistic nature of event of finding the elementary consistent particle in specified interfered wave, and hence the mathematical representation of this interfered wave should take into account the value of probability amplitude of finding an elementary particle inside the region occupied specified interfered wave. In quantum theory this probability amplitude corresponds to complex amplitude of the wave function of interfered wave. Also in Hilbert’s representation of the quantum theory these wave functions are representing the components of the quantum state vector. In this paper the author will develop the transformation theory of the region-like quantum state of the quantum system.

Direct characteristic-function tomography of the quantum states of quantum fields

Herein,we propose a novel strategy for implementing a direct readout of the symmetric characteristic function of the quantum states of quantum fields without the involvement of idealized measurements,an aspect that has always been deemed ill-defined in quantum field theory.This proposed scheme relies on the quantum control and measurements of an auxiliary qubit locally coupled to the quantum fields.By mapping the expectation values of both the real and imaginary parts of the field displacement operator to the qubit states,the qubit's readout provides complete information regarding the symmetric characteristic function.We characterize our technique by applying it to the Kubo-Martin-Schwinger(thermal)and squeezed states of a quantum scalar field.In addition,we have discussed general applications of this approach to analogue-gravity systems,such as Bose-Einstein condensates,within the scope of state-of-the-art experimental capabilities.This proposed strategy may serve as an essential in understanding and optimizing the control of quantum fields for relativistic quantum information applications,particularly in exploring the interplay between gravity and quantum,for example,the relation to locality,causality,and information.

Quantum Unruh Effect on Radiation of Black Holes

The quantum Unruh effect on radiation of a gravitational object including a black hole is analyzed and calculated. It is surprisingly found that the well-known Hawking radiation of a black hole is not physical. Applying the Stephan-Boltzmann law with the use of the Unruh radiation temperature at the surface of a black hole to calculate the power of radiation of the black hole is conceptually unphysical. This is because the Unruh radiation temperature results from the gravitational field of the object rather than from the thermal motion of matter of the object, so that the Stephan-Boltzmann law is not applicable. This paper shows that the emission power of Unruh radiation from a gravitational object should be calculated in terms of the rate of increase of the total Unruh radiation energy outside the object. The result obtained from this study indicates that a gravitational object can emit Unruh radiation when the variation of its mass and radius satisfies an inequality of dM/M > 1.25dR/R. For a black hole, the emission of Unruh radiation does not occur unless it can loose its mass (dM < 0). The emission power of Unruh radiation is only an extremely tiny part of the rate of mass-energy loss if the black hole is not extremely micro-sized. This study turns down our traditional understanding of the Hawking radiation and thermodynamics of black holes.

Between Quantum Mechanics and General Relativity

The origin of elementary particle mass is considered as a function of n-valued graviton quanta. To develop this concept we begin in a cold region of “empty space” comprised of only microscopic gravitons oscillating at angular frequency ω. From opposite directions enters a pair of stray protons. Upon colliding, heat and energy are released. Customarily, this phase and what follows afterward would be described by Quantum Chromodynamics (QCD). Instead, we argue for an intermediary step. One in which neighboring gravitons absorb discrete amounts of plane-wave energy. Captured by the graviton, the planewave becomes a standing wave, whereupon its electromagnetic energy densities are converted into gravitational quanta. Immediately thereafter an elementary particle is formed and emitted, having both mass and spin. From absorption to conversion to emission occurs in less than 3.7 × 10−16 s. During this basic unit of hybrid time, general relativity and quantum physics unite into a common set of physical laws. As additional stray protons collide the process continues. Over eons, vast regions of spacetime become populated with low-mass particles. These we recognize to be dark matter by its effects on large scale structures in the universe. Its counterpart, dark energy, arises when the conversion of gravitational quanta to particle emission is interrupted. This causes the gravitational quanta to be ejected. It is recognized by its large scale effects on the universe.

Conformal Quantum Field Theory and Subfactors

We survey a recent progress on algebraic quantum field theory in connection with subfactor theory. We mainly concentrate on one-dimensional conformal quantum field theory.