On the Annihilation of Electrons and Protons

1930 ◽  
Vol 26 (3) ◽  
pp. 361-375 ◽  
Author(s):  
P. A. M. Dirac
Keyword(s):  
Quantum Theory ◽  
Kinetic Energy ◽  
Energy Distribution ◽  
Physical Meaning ◽  
Negative Energy ◽  
The Other ◽  
Exclusion Principle ◽  
Positive Energy ◽  
Frequency Of Occurrence ◽  
Negative Energy States

An electron, according to relativity quantum theory, has two different kinds of states of motion, those for which the kinetic energy is positive and those for which it is negative. Only the former, of course, can correspond to actual electrons as observed in the laboratory. The latter, however, must also have a physical meaning, since the theory predicts that transitions will take place from one kind to the other. It has recently been proposed that one should assume that nearly all the possible states of negative energy are occupied, with just one electron in each state in accordance with Pauli's exclusion principle, and that the unoccupied states or ‘holes’ in the negative-energy distribution should be regarded as protons. According to these ideas, when an electron of positive energy makes a transition into one of the unoccupied negative-energy states, we have an electron and proton disappearing simultaneously, their energy being emitted in the form of electromagnetic radiation. The object of the present paper is to calculate the frequency of occurrence of these processes of annihilation of electrons and protons.

Discussion of the infinite distribution of electrons in the theory of the positron

1934 ◽  
Vol 30 (2) ◽  
pp. 150-163 ◽  
Author(s):  
P. A. M. Dirac
Keyword(s):  
Quantum Theory ◽  
Kinetic Energy ◽  
Negative Energy ◽  
The Other ◽  
Exclusion Principle ◽  
Negative Energy States ◽  
The World ◽  
Energy States

The quantum theory of the electron allows states of negative kinetic energy as well as the usual states of positive kinetic energy and also allows transitions from one kind of state to the other. Now particles in states of negative kinetic energy are never observed in practice. We can get over this discrepancy between theory and observation by assuming that, in the world as we know it, nearly all the states of negative kinetic energy are occupied, with one electron in each state in accordance with Pauli's exclusion principle, and that the distribution of negative-energy electrons is unobservable to us on account of its uniformity. Any unoccupied negative-energy states would be observable to us, as holes in the distribution of negative-energy electrons, but these holes would appear as particles with positive kinetic energy and thus not as things foreign to all our experience. It seems reasonable and in agreement with all the facts known at present to identify these holes with the recently discovered positrons and thus to obtain a theory of the positron.

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.

scholarly journals Bargmann–Wigner formulation and superradiance problem of bosons and fermions in Kerr space–time

2015 ◽  
Vol 30 (11) ◽  
pp. 1550052 ◽  
Author(s):  
Masakatsu Kenmoku ◽  
Y. M. Cho
Keyword(s):  
Negative Energy ◽  
Space Time ◽  
The Other ◽  
Positive Energy ◽  
Independent Components ◽  
Consistent Description ◽  
Other Hand ◽  
Kerr Space

The superradiance phenomena of massive bosons and fermions in the Kerr space–time are studied in the Bargmann–Wigner formulation. In case of bi-spinor, the four independent components spinors correspond to the four bosonic freedom: one scalar and three vectors uniquely. The consistent description of the Bargmann–Wigner equations between fermions and bosons shows that the superradiance of the type with positive energy (0 < ω) and negative momentum near horizon (p H < 0) is shown not to occur. On the other hand, the superradiance of the type with negative energy (ω < 0) and positive momentum near horizon (0 < p H ) is still possible for both scalar bosons and spinor fermions.

Some aspects of energy metabolism of the sow during pregnancy

1971 ◽  
Vol 13 (4) ◽  
pp. 677-683 ◽  
Author(s):  
M. W. A. Verstegen ◽  
A. J. H. van Es ◽  
H. J. Nijkamp
Keyword(s):  
Energy Requirement ◽  
Live Weight ◽  
Negative Energy ◽  
The Other ◽  
Positive Energy ◽  
Dietary Energy ◽  
Respiration Chamber ◽  
Dietary Energy Intake ◽  
Energy Balances ◽  
Balance Trials

SUMMARYSixteen energy and N-balance trials with six sows were performed to study the energy requirement and protein gain of the animals during different stages in the second half of pregnancy. Energy and N-balances were measured during periods of 1 week and gaseous exchange was measured in a respiration chamber. The animals received 2·0,2·5,2·75 or 3 0 kg/day of a normal concentrate ration for sows. In one experiment, one animal had a negative energy balance on the 2 kg ration in the sixth week of pregnancy but in the other experiments the dietary energy intake was sufficient for positive energy balances until a few days before parturition. The N-balances were about 20 to 32 g/day in the second half of the gestation period. With 2·5 and 2·75 kg feed there was a negative deposition of fat at about 2 weeks before parturition. Heat production increased during pregnancy, but at a greater rate during the last 2 weeks. Until 2 to 3 weeks before parturition 2·5 to 2·75 kg of feed seemed to be adequate to meet the energy requirement of a pregnant sow of 180–200 kg live weight. During the last 2 weeks 3 kg was sufficient.

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.

The energy distribution resulting from an impact on a floating body

2000 ◽  
Vol 417 ◽  
pp. 157-181 ◽  
Author(s):  
A. A. KOROBKIN ◽  
D. H. PEREGRINE
Keyword(s):  
Kinetic Energy ◽  
Energy Distribution ◽  
Water Flow ◽  
Compression Wave ◽  
The Body ◽  
The Other ◽  
Body Motion ◽  
Floating Body ◽  
Pressure Impulse ◽  
Work Done

The initial stage of the water flow caused by an impact on a floating body is considered. The vertical velocity of the body is prescribed and kept constant after a short acceleration stage. The present study demonstrates that impact on a floating and non-flared body gives acoustic effects that are localized in time behind the front of the compression wave generated at the moment of impact and are of major significance for explaining the energy distribution throughout the water, but their contribution to the flow pattern near the body decays with time. We analyse the dependence on the body acceleration of both the water flow and the energy distribution – temporal and spatial. Calculations are performed for a half-submerged sphere within the framework of the acoustic approximation. It is shown that the pressure impulse and the total impulse of the flow are independent of the history of the body motion and are readily found from pressure-impulse theory. On the other hand, the work done to oppose the pressure force, the internal energy of the water and its kinetic energy are essentially dependent on details of the body motion during the acceleration stage. The main parameter is the ratio of the time scale for the acoustic effects and the duration of the acceleration stage. When this parameter is small the work done to accelerate the body is minimal and is spent mostly on the kinetic energy of the flow. When the sphere is impulsively started to a constant velocity (the parameter is infinitely large), the work takes its maximum value: Longhorn (1952) discovered that half of this work goes to the kinetic energy of the flow near the body and the other half is taken away with the compression wave. However, the work required to accelerate the body decreases rapidly as the duration of the acceleration stage increases. The optimal acceleration of the sphere, which minimizes the acoustic energy, is determined for a given duration of the acceleration stage. Roughly speaking, the optimal acceleration is a combination of both sudden changes of the sphere velocity and uniform acceleration.If only the initial velocity of the body is prescribed and it then moves freely under the influence of the pressure, the fraction of the energy lost in acoustic waves depends only on the ratio of the body's mass to the mass of water displaced by the hemisphere.

scholarly journals Relativistic Brueckner-Hartree-Fock Theory in Infinite Nuclear Matter

2021 ◽  
Vol 252 ◽  
pp. 02001
Author(s):  
Peter Ring ◽  
Sibo Wang ◽  
Qiang Zhao ◽  
Jie Meng
Keyword(s):  
Nuclear Matter ◽  
Complete Solution ◽  
Negative Energy ◽  
The Other ◽  
Positive Energy ◽  
Density Functionals ◽  
Matrix Elements ◽  
Hartree Fock ◽  
Microscopic Derivation ◽  
Covariant Density

On the way of a microscopic derivation of covariant density functionals, the first complete solution of the relativistic Brueckner-Hartree-Fock (RBHF) equations is presented for symmetric nuclear matter. In most of the earlier investigations, the G-matrix is calculated only in the space of positive energy solutions. On the other side, for the solution of the relativistic Hartree-Fock (RHF) equations, also the elements of this matrix connecting positive and negative energy solutions are required. So far, in the literature, these matrix elements are derived in various approximations. We discuss solutions of the Thompson equation for the full Dirac space and compare the resulting equation of state with those of earlier attempts in this direction.

scholarly journals ON BOGOLIUBOV TRANSFORMATION OF SCALAR WAVE FUNCTIONS IN DE SITTER SPACE

1994 ◽  
Vol 09 (39) ◽  
pp. 3673-3684 ◽  
Author(s):  
HARU-TADA SATO ◽  
HISAO SUZUKI
Keyword(s):  
Hypergeometric Functions ◽  
Integral Relation ◽  
De Sitter Space ◽  
Negative Energy ◽  
Wave Functions ◽  
The Other ◽  
Bogoliubov Transformation ◽  
Scalar Wave ◽  
De Sitter ◽  
Negative Energy States

We discuss the Bogoliubov transformation of the scalar wave functions caused by the change of coordinates in four-dimensional de Sitter space. It is shown that the exact Bogoliubov coefficients can be obtained from the global coordinates to the static coordinates where there exists manifest horizon. We consider two types of global coordinates. In one global coordinates, it is shown that the Bogoliubov transformation to the static coordinates can be expressed by the discontinuous integral of Weber and Schafheitlin. The positive and negative energy states in the global coordinates degenerate in the static coordinates. In the other global coordinates, we obtain the Bogoliubov coefficients by using the analytic continuation of the hypergeometric functions in two variables. We also discuss the relation between two types of global coordinates and find an integral relation between the mode functions.

scholarly journals Polymer quantization, stability and higher-order time derivative terms

2016 ◽  
Vol 31 (09) ◽  
pp. 1650040 ◽  
Author(s):  
Patricio Cumsille ◽  
Carlos M. Reyes ◽  
Sebastian Ossandon ◽  
Camilo Reyes
Keyword(s):  
Field Theory ◽  
Stability Problem ◽  
Time Derivative ◽  
Negative Energy ◽  
Higher Order ◽  
The Other ◽  
Harmonic Oscillators ◽  
Positive Energy ◽  
Quantum Field ◽  
The Stability

The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a natural regulator for ultraviolet singularities arising in quantum field theory has been intensively studied. Here, along the same expectations, we investigate whether a nonstandard representation called polymer representation can smooth away the large amount of negative energy that afflicts the Hamiltonians of higher-order time derivative theories, rendering the theory unstable when interactions come into play. We focus on the fourth-order Pais–Uhlenbeck model which can be reexpressed as the sum of two decoupled harmonic oscillators one producing positive energy and the other negative energy. As expected, the Schrödinger quantization of such model leads to the stability problem or to negative norm states called ghosts. Within the framework of polymer quantization we show the existence of new regions where the Hamiltonian can be defined well bounded from below.

scholarly journals Quasi-Static and Steady-State Pictures for Collapsing Core of Type II Supernova

1988 ◽  
Vol 108 ◽  
pp. 420-421
Author(s):  
D. Sugimoto ◽  
A. Sasaki ◽  
T. Ebisuzaki
Keyword(s):  
Shock Wave ◽  
Steady State ◽  
Bound State ◽  
Negative Energy ◽  
Gravitational Energy ◽  
The Other ◽  
Positive Energy ◽  
Core Collapse ◽  
Type Ii ◽  
The Core

Explosion of type II supernova is, in principle, a difficult process: The presupernova star was in gravitationally bound state with negative energy but it has to be divided into two parts, the collapsed core of still lower (negative) energy and the ejected envelope of positive energy. This process is against nature in the sense most of the phenomena in nature proceed towards equipartition of energies. Thus, some finely tuned mechanism should be necessary for successful explosion. Two different mechanisms have been proposed; one is the prompt explosion where the gravitational energy release by the core collapse is transferred to the mantle by a shock wave, and the other is delayed explosion where it is transferred slowly by neutrinos diffusing out of the core. In what follows we shall concentrate in the case of the delayed explosion.

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