scholarly journals DIRAC SEA AND HOLE THEORY FOR BOSONS I: A NEW FORMULATION OF QUANTUM FIELD THEORIES

2008 ◽  
Vol 23 (18) ◽  
pp. 2733-2769 ◽  
Author(s):  
YOSHINOBU HABARA ◽  
YUKINORI NAGATANI ◽  
HOLGER B. NIELSEN ◽  
MASAO NINOMIYA
Keyword(s):  
Vacuum State ◽  
Negative Energy ◽  
Quantum Field Theories ◽  
Second Quantization ◽  
Hole Theory ◽  
Boson Case ◽  
Consistent Manner ◽  
Dirac Sea ◽  
New Formulation ◽  
Supersymmetric Theories

Bosonic formulation of the negative energy sea, so-called Dirac sea, is proposed by constructing a hole theory for bosons as a new formulation of the second quantization of bosonic fields. The original idea of Dirac sea for fermions, where the vacuum state is considered as a state completely filled by fermions of negative energy and holes in the sea are identified as antiparticles, is extended to boson case in a consistent manner. The bosonic vacuum consists of a sea filled by negative energy bosonic states, while physical probabilities become always positive definite. We introduce a method of the double harmonic oscillator to formulate the hole theory of bosons. Our formulation is also applicable to supersymmetric field theory. The sea for supersymmetric theories has an explicit supersymmetry. We suggest applications of our formulations to the anomaly theories and the string theories.

scholarly journals BOSON SEA VERSUS DIRAC SEA: GENERAL FORMULATION OF THE BOSON SEA THROUGH SUPERSYMMETRY

2004 ◽  
Vol 19 (32) ◽  
pp. 5561-5583 ◽  
Author(s):  
YOSHINOBU HABARA ◽  
HOLGER B. NIELSEN ◽  
MASAO NINOMIYA
Keyword(s):  
Harmonic Oscillator ◽  
Negative Energy ◽  
Positive Energy ◽  
Second Quantization ◽  
Negative Energy States ◽  
Quantization Formalism ◽  
Dirac Sea ◽  
Energy States ◽  
Physical Result ◽  
Usual Formalism

We consider the long standing problem in field theories of bosons that the boson vacuum does not consist of a "sea," unlike the fermion vacuum. We show with the help of supersymmetry considerations that the boson vacuum indeed does also consist of a sea in which the negative energy states are all "filled," analogous to the Dirac sea of the fermion vacuum, and that a hole produced by the annihilation of one negative energy boson is an antiparticle. Here, we must admit that it is only possible if we allow — as occurs in the usual formalism anyway — that the "Hilbert space" for the single particle bosons is not positive definite. This might be formally coped with by introducing the notion of a double harmonic oscillator, which is obtained by extending the condition imposed on the wave function. This double harmonic oscillator includes not only positive energy states but also negative energy states. We utilize this method to construct a general formalism for a boson sea analogous to the Dirac sea, irrespective of the existence of supersymmetry. The physical result is consistent with that of the ordinary second quantization formalism. We finally suggest applications of our method to the string theories.

scholarly journals DIRAC SEA AND HOLE THEORY FOR BOSONS II: RENORMALIZATION APPROACH

2008 ◽  
Vol 23 (18) ◽  
pp. 2771-2781 ◽  
Author(s):  
YOSHINOBU HABARA ◽  
YUKINORI NAGATANI ◽  
HOLGER B. NIELSEN ◽  
MASAO NINOMIYA
Keyword(s):  
Preceding Paper ◽  
Negative Energy ◽  
Positive Definite ◽  
Inner Product ◽  
Hole Theory ◽  
Negative Energy States ◽  
Analytical Properties ◽  
Dirac Sea ◽  
Renormalization Method ◽  
Renormalization Approach

In bosonic formulation of the negative energy sea, so-called Dirac sea presented in the preceding paper [arXiv:hep-th/0603242], one of the crucial points is how to construct a positive definite inner product in the negative energy states, since naive attempts would lead to nonpositive definite ones. In the preceding paper, the nonlocal method is used to define the positive definite inner product. In the present paper we, make use of a kind of ∊-regularization and renormalization method which may clarify transparently the analytical properties of our formulation.

scholarly journals Correlations in geometric states

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Wu-zhong Guo
Keyword(s):  
Central Charge ◽  
Convex Combination ◽  
Vacuum State ◽  
Quantum Correlations ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Classical Geometry ◽  
Accessible Information ◽  
Classical Correlations ◽  
Quantum And Classical Correlations

Abstract In this paper we explore the correlations in the geometric states. Here the geometric state means the state in CFTs that can be effectively described by classical geometry in the bulk in the semi-classical limit G → 0. By using the upper bound of Holevo information we show the convex combination of geometric states cannot be a geometric state. To understand the duality between thermofield double state and eternal black hle, we construct several correlated states of two CFTs. In all the examples we show their correlations are too weak to produce the a connected spacetime. Then we review the measure named quantum discord and use it to characterize the classical and quantum correlations in quantum field theories. Finally, we discuss the correlations between two intervals A and B with distance d in the vacuum state of 2D CFTs with large central charge c. The feature is the phase transition of the mutual information I (ρAB). We analyse the quasi-product state of ρAB for large d. By using the Koashi-Winter relation of tripartite states the quantum and classical correlations between A and B can expressed as Holevo information, which provides a new understanding of the correlations as accessible information.

Algebra of Superalgebraic Spinors as Algebra of Second Quantization of Fermions

2021 ◽  
pp. 165-187
Author(s):  
Vadim Monakhov ◽  
Alexey Kozhedub
Keyword(s):  
State Vector ◽  
Vacuum State ◽  
Charge Conjugation ◽  
Time Inversion ◽  
Second Quantization ◽  
Continuous Space

We developed the theory of superalgebraic spinors, which is based on the use of Grassmann densities and derivatives with respect to them in a pseudo-continuous space of momenta. The algebra that they form corresponds to the algebra of second quantization of fermions. We have constructed a vacuum state vector and have shown that it is symmetric with respect to $P$, $CT$ and $CPT$ transformations. Operators $C$ and $T$ transforms the vacuum into an alternative one. Therefore, time inversion $T$ and charge conjugation $C$ cannot be exact symmetries of the spinors.

RENORMALIZATION AND BOLTZMANN EQUATIONS IN THERMAL QUANTUM FIELD THEORY

1995 ◽  
Vol 10 (11) ◽  
pp. 1693-1700 ◽  
Author(s):  
H. CHU ◽  
H. UMEZAWA
Keyword(s):  
Boltzmann Equation ◽  
Renormalization Scheme ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Boltzmann Equations ◽  
Self Energy ◽  
Spatially Inhomogeneous ◽  
Thermo Field Dynamics ◽  
Self Consistent ◽  
Consistent Manner

The renormalization scheme in nonequilibrium thermal quantum field theories is reexamined. Instead of the self-energy diagonalization scheme, we propose to diagonalize Green’s function at equal time. This eliminates the problem of on-shell definition related to time-dependent energies and spatially inhomogeneous situations, and yields a Boltzmann equation that contains memory effect. The new diagonalization scheme and the derivation of the Boltzmann equation from it can be applied to any thermal situation. It allows the treatment of a nonequilibrium problem beyond perturbational calculations in a self-consistent manner. The results are applicable to both thermo field dynamics and the closed time path formalism.

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 SUPERSYMMETRIC RELATIVISTIC QUANTUM MECHANICS

2006 ◽  
Vol 21 (06) ◽  
pp. 1333-1340 ◽  
Author(s):  
YOSHINOBU HABARA ◽  
HOLGER B. NIELSEN ◽  
MASAO NINOMIYA
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Equations Of Motion ◽  
Relativistic Quantum Mechanics ◽  
Chiral Multiplet ◽  
Second Quantization ◽  
Matrix Formulation ◽  
The Matrix ◽  
Particle Level ◽  
Dirac Sea

We present an attempt to formulate the supersymmetric and relativistic quantum mechanics in the sense of realizing supersymmetry on the single particle level, by utilizing the equations of motion which is equivalent to the ordinary second quantization of the chiral multiplet. The matrix formulation is used to express the operators such as supersymmetry generators and fields of the chiral multiplets. We realize supersymmetry prior to filling the Dirac sea.

scholarly journals Dirac Sea for Bosons. I: -- Formulation of Negative Energy Sea for Bosons --

2005 ◽  
Vol 113 (3) ◽  
pp. 603-624 ◽  
Author(s):  
H. B. Nielsen ◽  
M. Ninomiya
Keyword(s):  
Negative Energy ◽  
Dirac Sea
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