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 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 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 Negative energy states in the Reissner–Nordström metric

2021 ◽  
pp. 2150120
Author(s):  
O. B. Zaslavskii
Keyword(s):  
Turning Point ◽  
High Energy ◽  
Negative Energy ◽  
Infinite Chain ◽  
White Hole ◽  
Negative Energy States ◽  
Energy Formula ◽  
High Energy Collisions ◽  
Energy States

We consider electrogeodesics on which the energy [Formula: see text] in the Reissner–Nordström metric. It is shown that outside the horizon there is exactly one turning point inside the ergoregion for such particles. This entails that such a particle passes through an infinite chain of black–white hole regions or terminates in the singularity. These properties are relevant for two scenarios of high energy collisions in which the presence of white holes is essential.

scholarly journals SUPERSYMMETRY AND THE DIRAC OSCILLATOR

1991 ◽  
Vol 06 (09) ◽  
pp. 1567-1589 ◽  
Author(s):  
C. QUESNE
Keyword(s):  
Ground State ◽  
Symmetry Algebra ◽  
Negative Energy ◽  
Dirac Oscillator ◽  
Relativistic Limit ◽  
First Order ◽  
Supersymmetric Partner ◽  
Negative Energy States ◽  
Pattern Characteristic ◽  
Supersymmetric Structure

We demonstrate the realization of supersymmetric quantum mechanics in the first-order Dirac oscillator equation by associating with it another Dirac equation, which may be considered as its supersymmetric partner. We show that both the particle and the antiparticle spectra, resulting from these two equations after filling the negative-energy states and redefining the physical ground state, indeed present the degeneracy pattern characteristic of unbroken supersymmetry. In addition, we analyze in detail two algebraic structures, each partially explaining the degeneracies present in the Dirac oscillator supersymmetric spectrum in the non-relativistic limit. One of them is the spectrum-generating superalgebra osp(2/2, ℝ), first proposed by Balantekin. We prove that it is closely connected with the supersymmetric structure of the first-order Dirac oscillator equation as its odd generators are the two sets of supercharges respectively associated with the equation and its supersymmetric partner. The other algebraic structure is an so(4)⊕so(3, 1) algebra, which is an extension of a similar algebra first considered by Moshinsky and Quesne. We prove that it is the symmetry algebra of the Dirac oscillator supersymmetric Hamiltonian. Some possible relations between the spectrum-generating superalgebra, the symmetry algebra, and their respective subalgebras are also suggested.

scholarly journals The vacuum in Dirac's theory of the positive electron

1934 ◽  
Vol 146 (857) ◽  
pp. 420-441 ◽  
Keyword(s):  
Kinetic Energy ◽  
Infinite Number ◽  
Strong Support ◽  
Negative Energy ◽  
Positive Energy ◽  
Quantum Mechanical ◽  
Normal Density ◽  
Physical Picture ◽  
Negative Energy States ◽  
Energy States

According to a theory proposed by Dirac one has to picture the vacuum as filled with an infinite number of electrons of negative kinetic energy, the electric density of which is, however, unobservable. One can observe only deviations from this "normal" density which either consist of an addition of electrons in states of positive energy or absence of electrons from some of the negative energy states (positive electrons). The discovery of the positive electron and the observed magnitude of the processes involving it give strong support to this view. This theory, as it stands, however, is not complete because it makes use of infinite quantities which are inadmissible in physical equations. It therefore must be understood (and was meant so by Dirac) to be a physical picture showing a way in which the quantum mechanical equations can probably be modified in order to give account of the positive electron and to solve the difficulty connected with the states of negative energy.

Inequalities between means of positive operators

1978 ◽  
Vol 83 (3) ◽  
pp. 393-401 ◽  
Author(s):  
K. V. Bhagwat ◽  
R. Subramanian
Keyword(s):  
Hilbert Space ◽  
Dimensional Space ◽  
Adjoint Operator ◽  
Positive Definite ◽  
Inner Product ◽  
Finite Dimensional Space ◽  
Finite Dimensional ◽  
Definite Operator ◽  
Unit Operator ◽  
Adjoint Operators

One of the most fruitful – and natural – ways of introducing a partial order in the set of bounded self-adjoint operators in a Hilbert space is through the concept of a positive operator. A bounded self-adjoint operator A denned on is called positive – and one writes A ≥ 0 - if the inner product (ψ, Aψ) ≥ 0 for every ψ ∈ . If, in addition, (ψ, Aψ) = 0 only if ψ = 0, then A is called positive-definite and one writes A > 0. Further, if there exists a real number γ > 0 such that A — γI ≥ 0, I being the unit operator, then A is called strictly positive (in symbols, A ≫ 0). In a finite dimensional space, a positive-definite operator is also strictly positive.

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