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Pohlmeyer Charge
In theoretical physics Pohlmeyer charge, named for Klaus Pohlmeyer, is a conserved charge invariant under the Virasoro algebra or its generalization. It can be obtained by expanding the holonomies (generating functions)Mikhailov, A. (2005)Geometry of fast moving strings :P\,Tr\, \exp i T_\mu\oint d\sigma A_\sigma^(\sigma) with respect to the constant matrices ''T''. The gauge field A_\sigma^\mu is defined as a combination of \partial X^\mu and its conjugate. According to the logic of loop quantum gravity and algebraic quantum field theory, these charges are the right physical quantities that should be used for quantization. This logic is however incompatible with the standard and well-established methods of quantum field theory based on Fock space and perturbation theory In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A cri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics. For example, while developing special relativity, Albert E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charge Invariance
Charge invariance refers to the fixed value of the electric charge of a particle regardless of its motion. Like mass, total spin and magnetic moment, particle's charge quantum number remains unchanged between two reference frames in relative motion. For example, an electron has a specific charge ''e'', total spin \tfrac, and invariant mass ''m''e. Accelerate that electron, and the charge, spin and mass assigned to it in all physical laws in the frame at rest and the moving frame remain the same – ''e'', \tfrac, ''m''e. In contrast, the particle's total relativistic energy or de Broglie wavelength change values between the reference frames. The origin of charge invariance, and all relativistic invariants, is presently unclear. There may be some hints proposed by string/M-theory. It is possible the concept of charge invariance may provide a key to unlocking the mystery of unification in physics – the single theory of gravity, electromagnetism, the strong, and weak nuclea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virasoro Algebra
In mathematics, the Virasoro algebra is a complex Lie algebra and the unique nontrivial central extension of the Witt algebra. It is widely used in two-dimensional conformal field theory and in string theory. It is named after Miguel Ángel Virasoro. Structure The Virasoro algebra is spanned by generators for and the central charge . These generators satisfy ,L_n0 and The factor of \frac is merely a matter of convention. For a derivation of the algebra as the unique central extension of the Witt algebra, see derivation of the Virasoro algebra or Schottenloher, Thm. 5.1, pp. 79. The Virasoro algebra has a presentation in terms of two generators (e.g. 3 and −2) and six relations. The generators L_ are called annihilation modes, while L_ are creation modes. A basis of creation generators of the Virasoro algebra's universal enveloping algebra is the set : \mathcal = \Big\_ For L\in \mathcal, let , L, = \sum_^k n_i, then _0,L= , L, L. Representation theory In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holonomy
In differential geometry, the holonomy of a connection on a smooth manifold is the extent to which parallel transport around closed loops fails to preserve the geometrical data being transported. Holonomy is a general geometrical consequence of the curvature of the connection. For flat connections, the associated holonomy is a type of monodromy and is an inherently global notion. For curved connections, holonomy has nontrivial local and global features. Any kind of connection on a manifold gives rise, through its parallel transport maps, to some notion of holonomy. The most common forms of holonomy are for connections possessing some kind of symmetry. Important examples include: holonomy of the Levi-Civita connection in Riemannian geometry (called Riemannian holonomy), holonomy of connections in vector bundles, holonomy of Cartan connections, and holonomy of connections in principal bundles. In each of these cases, the holonomy of the connection can be identified with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loop Quantum Gravity
Loop quantum gravity (LQG) is a theory of quantum gravity that incorporates matter of the Standard Model into the framework established for the intrinsic quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Albert Einstein's geometric formulation rather than the treatment of gravity as a mysterious mechanism (force). As a theory, LQG postulates that the structure of space and time is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale on the order of a Planck length, approximately 10−35 meters, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic structure. The areas of research, which involve about 30 research groups worldwide, share the basic physical assumptions and the mathematical description of quantum space. Research has evolved in two directions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Quantum Field Theory
Algebraic quantum field theory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic framework for quantum field theory, because it was introduced by . The axioms are stated in terms of an algebra given for every open set in Minkowski space, and mappings between those. Haag–Kastler axioms Let \mathcal be the set of all open and bounded subsets of Minkowski space. An algebraic quantum field theory is defined via a set \_ of von Neumann algebras \mathcal(O) on a common Hilbert space \mathcal satisfying the following axioms: * ''Isotony'': O_1 \subset O_2 implies \mathcal(O_1) \subset \mathcal(O_2). * ''Causality'': If O_1 is space-like separated from O_2, then mathcal(O_1),\mathcal(O_2)0. * ''Poincaré covariance'': A strongly continuous unitary representation U(\mathcal) of the Poincaré group \mathcal on \mathcal exists such that \mathcal(gO) = U(g) \mathcal(O) U(g)^*,\,\,g \in \mathcal. * ''Spectrum conditio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. The current standard model of particle physics is based on QFT. History Quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century. Its development began in the 1920s with the description of interactions between light and electrons, culminating in the first quantum field theory—quantum electrodynamics. A major theoretical obstacle soon followed with the appearance and persistence of various infinities in perturbative calculations, a problem only resolved in the 1950s with the invention of the renormalization procedure. A second major barrier came with QFT's apparent inabili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fock Space
The Fock space is an algebraic construction used in quantum mechanics to construct the quantum states space of a variable or unknown number of identical particles from a single particle Hilbert space . It is named after V. A. Fock who first introduced it in his 1932 paper "Konfigurationsraum und zweite Quantelung" (" Configuration space and second quantization"). M.C. Reed, B. Simon, "Methods of Modern Mathematical Physics, Volume II", Academic Press 1975. Page 328. Informally, a Fock space is the sum of a set of Hilbert spaces representing zero particle states, one particle states, two particle states, and so on. If the identical particles are bosons, the -particle states are vectors in a symmetrized tensor product of single-particle Hilbert spaces . If the identical particles are fermions, the -particle states are vectors in an antisymmetrized tensor product of single-particle Hilbert spaces (see symmetric algebra and exterior algebra respectively). A general state in Fock ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In regular perturbation theory, the solution is expressed as a power series in a small parameter The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of \varepsilon usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, often keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. The current standard model of particle physics is based on QFT. History Quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century. Its development began in the 1920s with the description of interactions between light and electrons, culminating in the first quantum field theory—quantum electrodynamics. A major theoretical obstacle soon followed with the appearance and persistence of various infinities in perturbative calculations, a problem only resolved in the 1950s with the invention of the renormalization procedure. A second major barrier came with QFT's apparent inabili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
