scholarly journals DISTORTIONS IN THE NEGATIVE ENERGY DIRAC SEA: VIOLATION OF THE GOTTFRIED SUM RULE AND $\Delta \bar u$ IN THE PROTON

2001 ◽  
Author(s):  
K. TSUSHIMA ◽  
A. W. THOMAS ◽  
G. V. DUNNE
Keyword(s):  
Negative Energy ◽  
Sum Rule ◽  
Dirac Sea

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 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

scholarly journals COMBINING THE TUNNELING AND ANOMALY PHENOMENA IN DERIVING THE GRAVITATIONAL ANOMALY

2009 ◽  
Vol 24 (32) ◽  
pp. 2639-2648 ◽  
Author(s):  
SUBIR GHOSH
Keyword(s):  
Black Hole ◽  
Energy Level ◽  
Hawking Radiation ◽  
Black Hole Physics ◽  
Negative Energy ◽  
Conformal Anomaly ◽  
Spectral Flow ◽  
Gravitational Anomaly ◽  
Zero Energy ◽  
Dirac Sea

In the present work we have derived the gravitational anomaly from a fundamentally different perspective: it emerges due to the tunneling of particles (in the present case fermions) across the black hole horizon. The latter effect is in fact the Hawking radiation. We have used the analogy of an early idea17,18 of visualizing chiral gauge anomaly as an effect of spectral flow of the energy levels, from the negative energy Dirac sea, across zero energy level in the presence of gauge interactions. This was extended to conformal anomaly in Ref. 23. In the present work, we exploit the latter formalism in black hole physics where we interpret crossing the horizon of black hole (the zero energy level) as a spectral flow since it is also accompanied by a change of sign in the energy of the particle. Furthermore, Hawking radiation induces a shrinking of the radius of the horizon15,16 which reminds us of a similar rearrangement in the Fermi level generated by the spectral flow.17,18,21 Hence in our formulation the negative energy states below horizon play a similar role as the Dirac sea. We successfully recover the gravitational anomaly.

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.

SUPERSYMMETRY, FOLDY-WOUTHUYSEN TRANSFORMATION AND STABILITY OF THE DIRAC SEA

1990 ◽  
Vol 05 (12) ◽  
pp. 949-954 ◽  
Author(s):  
MATÍAS MORENO ◽  
RODOLFO MARTÍNEZ ◽  
ARTURO ZENTELLA
Keyword(s):  
Magnetic Field ◽  
Dirac Equation ◽  
Closed Form ◽  
Large Class ◽  
Strong Coupling ◽  
Negative Energy ◽  
Strong Coupling Limit ◽  
Dirac Oscillator ◽  
Potential Problems ◽  
Dirac Sea

It is shown that for a large class of potential problems in the Dirac equation the positive and negative energy solutions do not mix even in the strong coupling limit We prove that this property, which implies a stability of the Dirac sea, is connected to the presence of superalgebra operators in the Dirac equation. The exact and closed form for the Foldy-Wouthuysen Hamiltonian which is used to prove this property are given. The potentials include the Dirac oscillator, the uniform time-independent magnetic field and the odd potentials and its nonabelian generalizations.

scholarly journals Effects of peroral alanine administration in lactating ewes with decreased availability of glucose

1997 ◽  
Vol 78 (5) ◽  
pp. 805-813 ◽  
Author(s):  
Kjell Holtenius ◽  
Paul Holtenius
Keyword(s):  
Fatty Acids ◽  
Plasma Level ◽  
Free Fatty Acids ◽  
Skeletal Muscles ◽  
Plasma Insulin ◽  
Glucose Oxidation ◽  
Negative Energy ◽  
Crossover Design ◽  
Metabolic Effects ◽  
Significant Elevation

The metabolic effects of a phlorizin-induced drainage of glucose were studied in six lactating ewes with or without peroral alanine drenches in a study of crossover design. Phlorizin gave rise to a small, but significant, elevation of plasma β-hydroxybutyrate. The plasma level of alanine decreased by about 30 % due to the phlorizin injections and alanine was negatively correlated to β-hydroxybutyrate. The plasma level of free fatty acids increased due to phlorizin. Plasma insulin and glucose concentrations were not significantly affected by phlorizin while glucagon level showed a small but significant increase. Peroral alanine drenches to phlorizin-treated ewes gave rise to a transitory elevation of alanine in plasma. The plasma level of free fatty acids was about 40 % lower in phlorizin-treated ewes receiving alanine and β-hydroxybutyrate tended to be lower (P < 0.08). We suggest that β-hydroxybutyrate, apart from its function as an oxidative fuel, might play an important role by limiting glucose oxidation and protein degradation in skeletal muscles during periods of negative energy balance in ruminants. Furthermore, it is suggested that alanine supplementation decreases lipolysis and ketogenesis in lactating ewes.

scholarly journals Cwebs beyond three loops in multiparton amplitudes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Neelima Agarwal ◽  
Lorenzo Magnea ◽  
Sourav Pal ◽  
Anurag Tripathi
Keyword(s):  
Gauge Theories ◽  
Anomalous Dimension ◽  
Wilson Line ◽  
Building Blocks ◽  
Feynman Diagrams ◽  
Loop Order ◽  
Abelian Gauge ◽  
Sum Rule ◽  
Combinatorial Properties ◽  
Low Dimensional

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

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