Physical Mathematics and the Future
... One thing led to another and, with a great boost from the resurgent interest in string theory, after 40-odd years of a flowering of intellectual endeavor a new field has emerged with its own distinctive character, its own aims and values, its own standards of proof. I like to refer to the subject as ...
... One thing led to another and, with a great boost from the resurgent interest in string theory, after 40-odd years of a flowering of intellectual endeavor a new field has emerged with its own distinctive character, its own aims and values, its own standards of proof. I like to refer to the subject as ...
slides
... Group Field Theories: spacetime from quantum discreteness to an amergent continuum – p. 4/3 models, simplicial QG,... ...
... Group Field Theories: spacetime from quantum discreteness to an amergent continuum – p. 4/3 models, simplicial QG,... ...
LHC Theory Lecture 1: Calculation of Scattering Cross Sections
... We know that the current j µ describes the interaction of electro-magnetic radiation with an external charge. At the fundamental level, this should be interpreted as the interaction of a photon with charged particles, such as electrons! ⇒ We need a relativistic field theory for fermions! Torsten Pfo ...
... We know that the current j µ describes the interaction of electro-magnetic radiation with an external charge. At the fundamental level, this should be interpreted as the interaction of a photon with charged particles, such as electrons! ⇒ We need a relativistic field theory for fermions! Torsten Pfo ...
Lecture notes
... What is the significance of topological order? Globel danicing pattern is a nice picture for topological order. But does it mean anything? Does topological order have any experiemntal significance? Does topological order have any new experiemntal properties, that is different from any symmetry brea ...
... What is the significance of topological order? Globel danicing pattern is a nice picture for topological order. But does it mean anything? Does topological order have any experiemntal significance? Does topological order have any new experiemntal properties, that is different from any symmetry brea ...
Sub-Planckian black holes and the Generalized Uncertainty Principle
... and the parameter β describing the GEH are independent. In this case, there are still subPlanckian black holes but the relationship between these and elementary particles becomes more complicated. The plan of this paper is a follows. In section 2 we discuss the concept of mass using the Komar integr ...
... and the parameter β describing the GEH are independent. In this case, there are still subPlanckian black holes but the relationship between these and elementary particles becomes more complicated. The plan of this paper is a follows. In section 2 we discuss the concept of mass using the Komar integr ...
In search of symmetry lost
... symmetries require the existence of appropriate gauge bosons, and vice versa. Through this connection between mathematics and physics — concept and reality — we arrive at a beautiful and tightly integrated theory of gauge bosons and their interactions with other forms of matter. A profound reflectio ...
... symmetries require the existence of appropriate gauge bosons, and vice versa. Through this connection between mathematics and physics — concept and reality — we arrive at a beautiful and tightly integrated theory of gauge bosons and their interactions with other forms of matter. A profound reflectio ...
Discrete Approaches to Quantum Gravity in Four Dimensions
... in theoretical physics still remains unsolved. This article contains an overview and a comprehensive bibliography of past efforts to define a consistent theory of quantum gravity in four dimensions via an intermediate discretization. I will only discuss models with some concrete implementation of th ...
... in theoretical physics still remains unsolved. This article contains an overview and a comprehensive bibliography of past efforts to define a consistent theory of quantum gravity in four dimensions via an intermediate discretization. I will only discuss models with some concrete implementation of th ...
Gravity in lower dimensions
... Dilaton X defined by its coupling to curvature R Kinetic term (∇X)2 contains coupling function U (X) Self-interaction potential V (X) leads to non-trivial geometries Gibbons–Hawking–York boundary term guarantees Dirichlet boundary problem for metric Hamilton–Jacobi counterterm contains superpotentia ...
... Dilaton X defined by its coupling to curvature R Kinetic term (∇X)2 contains coupling function U (X) Self-interaction potential V (X) leads to non-trivial geometries Gibbons–Hawking–York boundary term guarantees Dirichlet boundary problem for metric Hamilton–Jacobi counterterm contains superpotentia ...
Equivalence of Topological Codes and Fast Decoding
... to change encoding during a quantum computation. Because the mapping is local, this change will not propagate errors and is therefore fault-tolerant. This allows to put together the features of different codes—such as having transversal Clifford gates [7], lower weight stabilizer generators [6, 10, ...
... to change encoding during a quantum computation. Because the mapping is local, this change will not propagate errors and is therefore fault-tolerant. This allows to put together the features of different codes—such as having transversal Clifford gates [7], lower weight stabilizer generators [6, 10, ...
The Weak Force: From Fermi to Feynman
... to propagate, like the photons, with the speed of light. In any case their penetrating power exceeds many times that of photons of the same energy. It seems to me admissible that the neutrinos have spin 12 and that they obey Fermi statistics, even though experience does not provide us with any direc ...
... to propagate, like the photons, with the speed of light. In any case their penetrating power exceeds many times that of photons of the same energy. It seems to me admissible that the neutrinos have spin 12 and that they obey Fermi statistics, even though experience does not provide us with any direc ...
Three Roads To Quantum Gravity
... Heisenberg, Erwin SchroÈdinger, and many others. But this was only the starting point of the revolution, because neither of these two theories is complete enough to serve as a new foundation for physics. While very useful, and able to explain many things, each is incomplete and limited. Quantum theo ...
... Heisenberg, Erwin SchroÈdinger, and many others. But this was only the starting point of the revolution, because neither of these two theories is complete enough to serve as a new foundation for physics. While very useful, and able to explain many things, each is incomplete and limited. Quantum theo ...
Functional-Integral Representation of Quantum Field Theory {functint
... since the determinants on the right-hand sides are infinite. However, we shall see in Section 14.7, Eqs. (14.123)–(14.133), that correct finite partition functions are obtained if the infinities are removed by the method of dimensional regularization, that was used in Section 11.5 to remove divergen ...
... since the determinants on the right-hand sides are infinite. However, we shall see in Section 14.7, Eqs. (14.123)–(14.133), that correct finite partition functions are obtained if the infinities are removed by the method of dimensional regularization, that was used in Section 11.5 to remove divergen ...
View/Open
... the environment is retained. The effects from the environment on the quantum part are described by an embedding potential which is added to the electronic Hamiltonian. In this work, we present an extension of the open-ended response theory approach to include environment effects based on the polariza ...
... the environment is retained. The effects from the environment on the quantum part are described by an embedding potential which is added to the electronic Hamiltonian. In this work, we present an extension of the open-ended response theory approach to include environment effects based on the polariza ...
underdetermination and theory succession from the perspective of
... elementary particle physics model building is dominated by concepts which are either directly inspired by string theory, like the concept of large extra dimensions, or, like supersymmetry, gain authority from the claim that they are implied by string theory. Many recent cosmological models are also ...
... elementary particle physics model building is dominated by concepts which are either directly inspired by string theory, like the concept of large extra dimensions, or, like supersymmetry, gain authority from the claim that they are implied by string theory. Many recent cosmological models are also ...
Recently an undergraduate engineering student asked me if
... Theorem: No finistic, logical algorithm can be constructed to carry out Hilbert’s program even for a system of axioms as rudimentary as arithmetic, e.g., if x = y then y = x, and so on. Before committing suicide, Alan Turing picked this result up in the language of software and computers. Computers ...
... Theorem: No finistic, logical algorithm can be constructed to carry out Hilbert’s program even for a system of axioms as rudimentary as arithmetic, e.g., if x = y then y = x, and so on. Before committing suicide, Alan Turing picked this result up in the language of software and computers. Computers ...
Detailed information may be found here
... later to be called physics. Yet it is strangely modern: It is in fact fully relativistic (and was so long before Einstein); it is usually taught before quantum mechanics, yet many of the tools usually only properly taught in quantum mechanics have essential uses in electrodynamics (were in fact inve ...
... later to be called physics. Yet it is strangely modern: It is in fact fully relativistic (and was so long before Einstein); it is usually taught before quantum mechanics, yet many of the tools usually only properly taught in quantum mechanics have essential uses in electrodynamics (were in fact inve ...
Quantum gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe the force of gravity according to the principles of quantum mechanics.The current understanding of gravity is based on Albert Einstein's general theory of relativity, which is formulated within the framework of classical physics. On the other hand, the nongravitational forces are described within the framework of quantum mechanics, a radically different formalism for describing physical phenomena based on probability. The necessity of a quantum mechanical description of gravity follows from the fact that one cannot consistently couple a classical system to a quantum one.Although a quantum theory of gravity is needed in order to reconcile general relativity with the principles of quantum mechanics, difficulties arise when one attempts to apply the usual prescriptions of quantum field theory to the force of gravity. From a technical point of view, the problem is that the theory one gets in this way is not renormalizable and therefore cannot be used to make meaningful physical predictions. As a result, theorists have taken up more radical approaches to the problem of quantum gravity, the most popular approaches being string theory and loop quantum gravity. A recent development is the theory of causal fermion systems which gives quantum mechanics, general relativity, and quantum field theory as limiting cases.Strictly speaking, the aim of quantum gravity is only to describe the quantum behavior of the gravitational field and should not be confused with the objective of unifying all fundamental interactions into a single mathematical framework. While any substantial improvement into the present understanding of gravity would aid further work towards unification, study of quantum gravity is a field in it's own right with various branches having different approaches to unification. Although some quantum gravity theories, such as string theory, try to unify gravity with the other fundamental forces, others, such as loop quantum gravity, make no such attempt; instead, they make an effort to quantize the gravitational field while it is kept separate from the other forces. A theory of quantum gravity that is also a grand unification of all known interactions is sometimes referred to as a theory of everything (TOE).One of the difficulties of quantum gravity is that quantum gravitational effects are only expected to become apparent near the Planck scale, a scale far smaller in distance (equivalently, far larger in energy) than what is currently accessible at high energy particle accelerators. As a result, quantum gravity is a mainly theoretical enterprise, although there are speculations about how quantum gravity effects might be observed in existing experiments.