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 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.

scholarly journals Quantum Field Theory over $\mathbb{F}_q$

10.37236/589 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Oliver Schnetz
Keyword(s):  
Field Theory ◽  
Perturbation Series ◽  
The Other ◽  
Field Theories ◽  
Roots Of Unity ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Feynman Rules ◽  
Graph Hypersurfaces ◽  
Prime 2

We consider the number $\bar N(q)$ of points in the projective complement of graph hypersurfaces over $\mathbb{F}_q$ and show that the smallest graphs with non-polynomial $\bar N(q)$ have 14 edges. We give six examples which fall into two classes. One class has an exceptional prime 2 whereas in the other class $\bar N(q)$ depends on the number of cube roots of unity in $\mathbb{F}_q$. At graphs with 16 edges we find examples where $\bar N(q)$ is given by a polynomial in $q$ plus $q^2$ times the number of points in the projective complement of a singular K3 in $\mathbb{P}^3$. In the second part of the paper we show that applying momentum space Feynman-rules over $\mathbb{F}_q$ lets the perturbation series terminate for renormalizable and non-renormalizable bosonic quantum field theories.

scholarly journals NEGATIVE ENERGY DENSITIES IN QUANTUM FIELD THEORY

2010 ◽  
Vol 25 (11) ◽  
pp. 2355-2363 ◽  
Author(s):  
L. H. FORD
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Energy Density ◽  
Negative Energy ◽  
Mean Value ◽  
Quantum Field ◽  
Two Dimensional ◽  
Vacuum Fluctuations ◽  
Negative Energy Density ◽  
Dimensional Spacetime

Quantum field theory allows for the suppression of vacuum fluctuations, leading to sub-vacuum phenomena. One of these is the appearance of local negative energy density. Selected aspects of negative energy will be reviewed, including the quantum inequalities which limit its magnitude and duration. However, these inequalities allow the possibility that negative energy and related effects might be observable. Some recent proposals for experiments to search for sub-vacuum phenomena will be discussed. Fluctuations of the energy density around its mean value will also be considered, and some recent results on a probability distribution for the energy density in two dimensional spacetime are summarized.

THE CLASSICAL HARMONIC OSCILLATOR ON GALOIS AND P-ADIC FIELDS

1989 ◽  
Vol 04 (09) ◽  
pp. 2211-2233 ◽  
Author(s):  
YANNICK MEURICE
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Difference Equation ◽  
Harmonic Oscillator ◽  
Continuum Limit ◽  
The Other ◽  
Quantum Field ◽  
Real Numbers ◽  
Technical Tool ◽  
Classical Motion

Starting from a difference equation corresponding to the harmonic oscillator, we discuss various properties of the classical motion (cycles, conserved quantity, boundedness, continuum limit) when the dynamical variables take their values on Galois or p-adic fields. We show that these properties can be applied as a technical tool to calculate the motion on the real numbers. On the other hand, we also give an example where the motions over Galois and p-adic fields have a direct physical interpretation. Some perspectives for quantum field theory and strings are briefly discussed.

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 ON THE STABILITY OF COHERENT STATES FOR PAIS–UHLENBECK OSCILLATOR

2013 ◽  
Vol 28 (12) ◽  
pp. 1350038 ◽  
Author(s):  
SOUVIK PRAMANIK ◽  
SUBIR GHOSH
Keyword(s):  
Coherent States ◽  
Uncertainty Relation ◽  
Energy Levels ◽  
Negative Energy ◽  
Positive Energy ◽  
Expectation Values ◽  
Higher Derivative ◽  
Identical Manner ◽  
Heisenberg Uncertainty ◽  
The Stability

We have constructed coherent states for the higher derivative Pais–Uhlenbeck Oscillator (PUO). In the process, we have suggested a novel way to construct coherent states for the oscillator having only negative energy levels. These coherent states have negative energies in general but their coordinate and momentum expectation values and dispersions behave in an identical manner as that of normal (positive energy) oscillator. The coherent states for the PUO have constant dispersions and a modified Heisenberg Uncertainty Relation. Moreover, under reasonable assumptions on parameters these coherent states can have positive energies.

scholarly journals Connected Chord Diagrams and Bridgeless Maps

10.37236/7400 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Julien Courtiel ◽  
Karen Yeats ◽  
Noam Zeilberger
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Lambda Calculus ◽  
The Other ◽  
Combinatorial Proof ◽  
Quantum Field ◽  
Technical Parameter ◽  
Simple Application ◽  
Chord Diagrams ◽  
Combinatorial Maps

We present a surprisingly new connection between two well-studied combinatorial classes: rooted connected chord diagrams on one hand, and rooted bridgeless combinatorial maps on the other hand. We describe a bijection between these two classes, which naturally extends to indecomposable diagrams and general rooted maps. As an application, this bijection provides a simplifying framework for some technical quantum field theory work realized by some of the authors. Most notably, an important but technical parameter naturally translates to vertices at the level of maps. We also give a combinatorial proof to a formula which previously resulted from a technical recurrence, and with similar ideas we prove a conjecture of Hihn. Independently, we revisit an equation due to Arquès and Béraud for the generating function counting rooted maps with respect to edges and vertices, giving a new bijective interpretation of this equation directly on indecomposable chord diagrams, which moreover can be specialized to connected diagrams and refined to incorporate the number of crossings. Finally, we explain how these results have a simple application to the combinatorics of lambda calculus, verifying the conjecture that a certain natural family of lambda terms is equinumerous with bridgeless maps.

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