The Yukawa Theory of Nuclear Forces in the Light of Present
... The Yukawa theory of nuclear force!llllbas led to many successes and, owing to the present state of quantum theory, to some d'ifficulties. Among the successes one remembers first the existence Of the 7Z'-meson and the possibility of desc.ribing the spin dependency and the saturation of nuclear force ...
... The Yukawa theory of nuclear force!llllbas led to many successes and, owing to the present state of quantum theory, to some d'ifficulties. Among the successes one remembers first the existence Of the 7Z'-meson and the possibility of desc.ribing the spin dependency and the saturation of nuclear force ...
Progress In N=2 Field Theory - Rutgers Physics
... With a great boost from string theory, after 40 years of intellectual ferment a new field has emerged with its own distinctive character, its own aims and values, its own standards of proof. One of the guiding principles is certainly Hilbert’s 6th Problem (generously interpreted): Discover the ultim ...
... With a great boost from string theory, after 40 years of intellectual ferment a new field has emerged with its own distinctive character, its own aims and values, its own standards of proof. One of the guiding principles is certainly Hilbert’s 6th Problem (generously interpreted): Discover the ultim ...
Emergence, Effective Field Theory, Gravitation and Nuclei
... consistent theory of quantum gravity valid at all distance scales. But such theories are hard to come by, and in any case, are not very relevant in practice. But as an open theory, quantum gravity is arguably our best quantum field theory, not the worst. …. {Here he describes the effective field the ...
... consistent theory of quantum gravity valid at all distance scales. But such theories are hard to come by, and in any case, are not very relevant in practice. But as an open theory, quantum gravity is arguably our best quantum field theory, not the worst. …. {Here he describes the effective field the ...
QUANTUM GEOMETRY OF BOSONIC STRINGS
... There are methods and formulae in science, which serve as master-keys to many apparently different problems. The resources o f such things have to be refilled from time to time. In my opinion at the present time we have to develop an art of handling sums over random surfaces. These sums replace the ...
... There are methods and formulae in science, which serve as master-keys to many apparently different problems. The resources o f such things have to be refilled from time to time. In my opinion at the present time we have to develop an art of handling sums over random surfaces. These sums replace the ...
The Klein-Gordon equation
... is not positive definite and vanishes even for real Φ(x) fully. The field Φ(x) is therefore not suitable as a probability amplitude! ...
... is not positive definite and vanishes even for real Φ(x) fully. The field Φ(x) is therefore not suitable as a probability amplitude! ...
Particle physics, from Rutherford to the LHC
... renormalization, of a finite number of parameters in the theory. But those infinities can be canceled by a redefinition of the infinite number of parameters in the theory. Moreover, to each order in perturbation theory one encounters only a finite number of free parameters, and only a finite number ...
... renormalization, of a finite number of parameters in the theory. But those infinities can be canceled by a redefinition of the infinite number of parameters in the theory. Moreover, to each order in perturbation theory one encounters only a finite number of free parameters, and only a finite number ...
CHAPTER 2. LAGRANGIAN QUANTUM FIELD THEORY §2.1
... (Even this first step is non-trivial, since products of fields are not always well defined due to their distributional nature. We will refine this step later, but for now we continue.) Since now Φ is a quantum operator we face our first problem in simply carrying over classical operations to the qua ...
... (Even this first step is non-trivial, since products of fields are not always well defined due to their distributional nature. We will refine this step later, but for now we continue.) Since now Φ is a quantum operator we face our first problem in simply carrying over classical operations to the qua ...
Presentazione di PowerPoint - INAF - OA
... The standard cosmology is a successful framework for interpreting observations. In spite of this fact there were certain questions which remained unsolved until 1980s. For many years it was assumed that any solution of these problems would have to await a theory of quantum gravity. The great success ...
... The standard cosmology is a successful framework for interpreting observations. In spite of this fact there were certain questions which remained unsolved until 1980s. For many years it was assumed that any solution of these problems would have to await a theory of quantum gravity. The great success ...
2. Free Fields
... so that, with this new definition, H |0i = 0. In fact, the difference between this Hamiltonian and the previous one is merely an ordering ambiguity in moving from the classical theory to the quantum theory. For example, if we defined the Hamiltonian of the harmonic oscillator to be H = (1/2)(ωq − ip ...
... so that, with this new definition, H |0i = 0. In fact, the difference between this Hamiltonian and the previous one is merely an ordering ambiguity in moving from the classical theory to the quantum theory. For example, if we defined the Hamiltonian of the harmonic oscillator to be H = (1/2)(ωq − ip ...
Scale invariance
In physics, mathematics, statistics, and economics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor. The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry.In mathematics, scale invariance usually refers to an invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilatations. It is also possible for the probability distributions of random processes to display this kind of scale invariance or self-similarity.In classical field theory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically describe classical physical processes with no characteristic length scale.In quantum field theory, scale invariance has an interpretation in terms of particle physics. In a scale-invariant theory, the strength of particle interactions does not depend on the energy of the particles involved.In statistical mechanics, scale invariance is a feature of phase transitions. The key observation is that near a phase transition or critical point, fluctuations occur at all length scales, and thus one should look for an explicitly scale-invariant theory to describe the phenomena. Such theories are scale-invariant statistical field theories, and are formally very similar to scale-invariant quantum field theories.Universality is the observation that widely different microscopic systems can display the same behaviour at a phase transition. Thus phase transitions in many different systems may be described by the same underlying scale-invariant theory.In general, dimensionless quantities are scale invariant. The analogous concept in statistics are standardized moments, which are scale invariant statistics of a variable, while the unstandardized moments are not.