EUBET 2014: Applications of effective field theories to particle
... We derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian and then taking the massless limit. The Berry connection naturally emerges in the diagonalization process to mod ...
... We derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian and then taking the massless limit. The Berry connection naturally emerges in the diagonalization process to mod ...
Decidable fragments of first-order logic Decidable fragments of first
... For r = 1, 2, let Tr be the set of all r -tables that are realized in A. Both sets are finite because Lϕ is finite. b n with universe Bn = {1, . . . , n} is The random Lϕ -structure B obtained as follows. (i) To each b in Bn , assign a 1-table Tb that is chosen uniformly at random from T1 . (ii) To ...
... For r = 1, 2, let Tr be the set of all r -tables that are realized in A. Both sets are finite because Lϕ is finite. b n with universe Bn = {1, . . . , n} is The random Lϕ -structure B obtained as follows. (i) To each b in Bn , assign a 1-table Tb that is chosen uniformly at random from T1 . (ii) To ...
Scientific Research
... •Nonzero integers are significant •Leading zeros are never significant •Captive zeros are always significant •Trailing zeros are only significant when there is a decimal present in the number ...
... •Nonzero integers are significant •Leading zeros are never significant •Captive zeros are always significant •Trailing zeros are only significant when there is a decimal present in the number ...
The characterization of ground states
... such systems. The fundamental qualitative feature of having fluid and solid phases, the latter appearing at low temperature and/or high pressure, can even be usefully modelled with classical statistical mechanics. Yet although this phase structure has been amply supported by computer simulations [F ...
... such systems. The fundamental qualitative feature of having fluid and solid phases, the latter appearing at low temperature and/or high pressure, can even be usefully modelled with classical statistical mechanics. Yet although this phase structure has been amply supported by computer simulations [F ...
Normal and anti-normal ordered expressions for
... Very recently, Fujii and Suzuki have shown ordering expressions for n̂k as different types of polynomials with respect to the number operator [3]. They have shown nontrivial relations including the use of Stirling numbers of the first kind [4]. Here we, do the opposite: we obtain an expression for n ...
... Very recently, Fujii and Suzuki have shown ordering expressions for n̂k as different types of polynomials with respect to the number operator [3]. They have shown nontrivial relations including the use of Stirling numbers of the first kind [4]. Here we, do the opposite: we obtain an expression for n ...
First-order logic;
... Representation: Understand the relationships between different representations of the same information or idea. I ...
... Representation: Understand the relationships between different representations of the same information or idea. I ...
Ehrenfest theorem, Galilean invariance and nonlinear Schr\" odinger
... Alkali gases. The equation is an effective equation, derivable from a field theory by taking condensate expectation values, and it has found quite success in the description of the BEC setup. Starting from a linear field theory of particles, it is possible to arrive at a nonlinear Schrödinger equat ...
... Alkali gases. The equation is an effective equation, derivable from a field theory by taking condensate expectation values, and it has found quite success in the description of the BEC setup. Starting from a linear field theory of particles, it is possible to arrive at a nonlinear Schrödinger equat ...
Chapter 8 Microcanonical ensemble
... Since Γ has arbitrary units, S is defined up to an arbitrary additive constant. In order to take into account the arbitrary constant, we write S as ...
... Since Γ has arbitrary units, S is defined up to an arbitrary additive constant. In order to take into account the arbitrary constant, we write S as ...
Propositional Logic
... algorithm in which resolution is embedded. • Can be made understandable to non-technical users • Needs to be combined with a search algorithm. • Can be very appropriate for general problem solving (e.g., using PROLOG) CSE 415 -- (c) S. Tanimoto, 2008 Propositional Logic ...
... algorithm in which resolution is embedded. • Can be made understandable to non-technical users • Needs to be combined with a search algorithm. • Can be very appropriate for general problem solving (e.g., using PROLOG) CSE 415 -- (c) S. Tanimoto, 2008 Propositional Logic ...
Mathematical Logic
... But... Formal proofs are bloated and over expanded! I find nothing in [formal logic] but shackles. It does not help us at all in the direction of conciseness, far from it; and if it requires 27 equations to establish that 1 is a number, how many will it require to demonstrate a real theorem? (Poinca ...
... But... Formal proofs are bloated and over expanded! I find nothing in [formal logic] but shackles. It does not help us at all in the direction of conciseness, far from it; and if it requires 27 equations to establish that 1 is a number, how many will it require to demonstrate a real theorem? (Poinca ...
Proof
... by the UFT they can’t be equal! Contradiction. • Because assuming that √2 is rational leads to a contradiction, √2 must be irrational. QED ...
... by the UFT they can’t be equal! Contradiction. • Because assuming that √2 is rational leads to a contradiction, √2 must be irrational. QED ...
MUltseq: a Generic Prover for Sequents and Equations*
... logics. This means that it takes as input the rules of a many-valued sequent calculus as well as a many-sided sequent and searches – automatically or interactively – for a proof of the latter. For the sake of readability, the output of MUltseq is typeset as a LATEX document. Though the sequent rules ...
... logics. This means that it takes as input the rules of a many-valued sequent calculus as well as a many-sided sequent and searches – automatically or interactively – for a proof of the latter. For the sake of readability, the output of MUltseq is typeset as a LATEX document. Though the sequent rules ...
The Simple Harmonic Oscillator
... harmonic oscillator potential yields an extremely simple set of energy eigenvalues: 1/2, 3/2, 5/2, and so on, in natural units. If instead you use the matrix diagonalization method, embedding the oscillator inside an infinite square well, it’s just a matter of centering the oscillator inside the inf ...
... harmonic oscillator potential yields an extremely simple set of energy eigenvalues: 1/2, 3/2, 5/2, and so on, in natural units. If instead you use the matrix diagonalization method, embedding the oscillator inside an infinite square well, it’s just a matter of centering the oscillator inside the inf ...
Notes on Propositional Logic
... In propositional logic, we would like to apply operators not only to atomic propositions, but also to the result of applying other operators. This means that our language of well-formed formulas in propositional logic should be inductively defined as follows. Definition 1. For a given set A of propo ...
... In propositional logic, we would like to apply operators not only to atomic propositions, but also to the result of applying other operators. This means that our language of well-formed formulas in propositional logic should be inductively defined as follows. Definition 1. For a given set A of propo ...
QUANTUM PARTICLES PASSING THROUGH A MATTER
... infinite wave front. Statistics could be performed directly on matter waves associated with the forward-going wave front and those diffracted at its edge. This makes it possible a new mechanism for the thermal interaction with the surround space at a finite temperature. The time-dependent internal e ...
... infinite wave front. Statistics could be performed directly on matter waves associated with the forward-going wave front and those diffracted at its edge. This makes it possible a new mechanism for the thermal interaction with the surround space at a finite temperature. The time-dependent internal e ...
Unit-1-B - WordPress.com
... The above sentence (p → q) states only that Raju will eat fruitsalad containing mangoes. It does not, however, rule out the possibility that Raju will eat fruit-salad containing apples. Whenever there is a statement p ↔ q (if and only if),its meaning is different from the previous one. This is equiv ...
... The above sentence (p → q) states only that Raju will eat fruitsalad containing mangoes. It does not, however, rule out the possibility that Raju will eat fruit-salad containing apples. Whenever there is a statement p ↔ q (if and only if),its meaning is different from the previous one. This is equiv ...
Measuring the Size of Elementary Particle Collisions
... Bosons are integer spin particles. Identical Bosons have a symmetric two particle wave function -any number may occupy a given quantum state... Photons and pions are examples of Bosons Fermions are half-integer spin particles. Identical Fermions have an antisymmetric wave function -only one particle ...
... Bosons are integer spin particles. Identical Bosons have a symmetric two particle wave function -any number may occupy a given quantum state... Photons and pions are examples of Bosons Fermions are half-integer spin particles. Identical Fermions have an antisymmetric wave function -only one particle ...
A systematic proof theory for several modal logics
... inferences where the concluding sequent contains exactly one formula. It is easily shown that the sequent formulation contains all the theorems of the Hilbert formulation, and with a little ingenuity, modelling the multisets by disjunctions, the reverse containment can also be demonstrated. We can a ...
... inferences where the concluding sequent contains exactly one formula. It is easily shown that the sequent formulation contains all the theorems of the Hilbert formulation, and with a little ingenuity, modelling the multisets by disjunctions, the reverse containment can also be demonstrated. We can a ...
PPT
... The waves have exactly the same form as standing waves on a string, sound waves in a pipe, etc. The wavelength is determined by the condition that it fits in the box. On a string the wave is a displacement y(x) and the square is the intensity, etc. The discrete set of allowed wavelengths results in ...
... The waves have exactly the same form as standing waves on a string, sound waves in a pipe, etc. The wavelength is determined by the condition that it fits in the box. On a string the wave is a displacement y(x) and the square is the intensity, etc. The discrete set of allowed wavelengths results in ...
Particle Physics on Noncommutative Spaces
... • However, by causality R cannot exceed t. • GR and causality imply: • Combined with the QM bound, they require x > 1 in Planck units or • This derivation was not specific to an interferometer - the result is device independent: no device subject to quantum mechanics, gravity and causality can excl ...
... • However, by causality R cannot exceed t. • GR and causality imply: • Combined with the QM bound, they require x > 1 in Planck units or • This derivation was not specific to an interferometer - the result is device independent: no device subject to quantum mechanics, gravity and causality can excl ...
Goldstone Bosons and Chiral Symmetry Breaking in QCD
... Now consider the limit pµ = 0. The first term on the right hand side becomes the matrix element of [Q a , Ob (0)] = O(0). This is non-zero. The second term must be singular, then, if the equation is to hold. This singularity, as we will now show, requires the presence of a massless particle. As in ...
... Now consider the limit pµ = 0. The first term on the right hand side becomes the matrix element of [Q a , Ob (0)] = O(0). This is non-zero. The second term must be singular, then, if the equation is to hold. This singularity, as we will now show, requires the presence of a massless particle. As in ...