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CPT-symmetry
Charge, parity, and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T). CPT is the only combination of C, P, and T that is observed to be an exact symmetry of nature at the fundamental level. The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry. In layman terms, this stipulates that an antimatter, mirrored, and time reversed universe would behave exactly the same as our regular universe. History The CPT theorem appeared for the first time, implicitly, in the work of Julian Schwinger in 1951 to prove the connection between spin and statistics. In 1954, Gerhart Lüders and Wolfgang Pauli derived more explicit proofs, so this theorem is sometimes known as the Lüders–Pauli theorem. At about the same time ...
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C-symmetry
In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-symmetry is an abbreviation of the phrase "charge conjugation symmetry", and is used in discussions of the symmetry of physical laws under charge-conjugation. Other important discrete symmetries are P-symmetry (parity) and T-symmetry (time reversal). These discrete symmetries, C, P and T, are symmetries of the equations that describe the known fundamental forces of nature: electromagnetism, gravity, the strong and the weak interactions. Verifying whether some given mathematical equation correctly models nature requires giving physical interpretation not only to continuous symmetries, such as motion in time, but also to its discrete symmetries, and then determining whether nature adheres to these symmetries. Unlike the continuous symmetri ...
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Charge Conjugation
In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-symmetry is an abbreviation of the phrase "charge conjugation symmetry", and is used in discussions of the symmetry of physical laws under charge-conjugation. Other important discrete symmetries are P-symmetry (parity) and T-symmetry (time reversal). These discrete symmetries, C, P and T, are symmetries of the equations that describe the known fundamental forces of nature: electromagnetism, gravity, the strong and the weak interactions. Verifying whether some given mathematical equation correctly models nature requires giving physical interpretation not only to continuous symmetries, such as motion in time, but also to its discrete symmetries, and then determining whether nature adheres to these symmetries. Unlike the continuous symm ...
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Symmetry In Physics
The symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. A family of particular transformations may be ''continuous'' (such as rotation of a circle) or ''discrete'' (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see ''Symmetry group''). These two concepts, Lie and finite groups, are the foundation for the fundamental theories of modern physics. Symmetries are frequently amenable to mathematical formulations such as group representations and can, in addition, be exploited to simplify many problems. Arguably the most important example of a symmetry in physics is that the speed of light has the same value in all frames of re ...
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Kongelige Danske Videnskabernes Selskab, Matematisk-Fysiske Meddelelser
The Royal Danish Academy of Sciences and Letters ({{Langx, da, Det Kongelige Danske Videnskabernes Selskab or ''Videnskabernes Selskab'') is a Danish academy of science. The Royal Danish Academy was established on 13 November 1742, and was created with the purpose of strengthening the position of Science in Denmark as well as promoting interdisciplinary understanding. The Royal Danish Academy works as a body of cooperation and a meeting place for prominent scientists from all areas of basic scientific research. Its core activities consist of organizing the biweekly meetings for the academy's members, publishing scientific works, advising, and communicating, organizing and conducting events and lectures of a scientific character (e.g. public lectures and symposiums) as well as participating in international cooperation with other scientific academies and with scientific organizations like for example ISC and EASAC. Since 1745, the Royal Danish Academy has had its own publishing c ...
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Imaginary Number
An imaginary number is the product of a real number and the imaginary unit , is usually used in engineering contexts where has other meanings (such as electrical current) which is defined by its property . The square (algebra), square of an imaginary number is . For example, is an imaginary number, and its square is . The number 0, zero is considered to be both real and imaginary. Originally coined in the 17th century by René Descartes as a derogatory term and regarded as fictitious or useless, the concept gained wide acceptance following the work of Leonhard Euler (in the 18th century) and Augustin-Louis Cauchy and Carl Friedrich Gauss (in the early 19th century). An imaginary number can be added to a real number to form a complex number of the form , where the real numbers and are called, respectively, the ''real part'' and the ''imaginary part'' of the complex number. History Although the Greek mathematician and engineer Heron of Alexandria is noted as the first t ...
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Lorentz Boost
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz. The most common form of the transformation, parametrized by the real constant v, representing a velocity confined to the -direction, is expressed as \begin t' &= \gamma \left( t - \frac \right) \\ x' &= \gamma \left( x - v t \right)\\ y' &= y \\ z' &= z \end where and are the coordinates of an event in two frames with the spatial origins coinciding at , where the primed frame is seen from the unprimed frame as moving with speed along the -axis, where is the speed of light, and \gamma = \frac is the Lorentz factor. When speed is much smaller than , the Lorentz factor is negligibly different from 1, but a ...
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CP-symmetry
In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (Charge (physics), charge conjugation symmetry) and Parity (physics), P-symmetry (Parity (physics), parity symmetry). CP-symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle (C-symmetry) while its spatial coordinates are inverted ("mirror" or P-symmetry). CP violation is only observed in the weak interaction. The discovery of CP violation in 1964 in the decays of neutral kaons resulted in the Nobel Prize in Physics in 1980 for its discoverers James Cronin and Val Fitch. CP violation was subsequently discovered in many other meson decays. In 2025, the LHCb experiment discovered CP violation in baryons. There is some evidence CP violation may occur in neutrino interactions. It is important to the matter-antimatter asymmetry problem, the strong CP problem, and in the study of weak interacti ...
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Weak Force
In nuclear physics and particle physics, the weak interaction, weak force or the weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, and gravitation. It is the mechanism of interaction between subatomic particles that is responsible for the radioactive decay of atoms: The weak interaction participates in nuclear fission and nuclear fusion. The theory describing its behaviour and effects is sometimes called quantum flavordynamics (QFD); however, the term QFD is rarely used, because the weak force is better understood by electroweak theory (EWT). The effective range of the weak force is limited to subatomic distances and is less than the diameter of a proton. Background The Standard Model of particle physics provides a uniform framework for understanding electromagnetic, weak, and strong interactions. An interaction occurs when two particles (typically, but not necessarily, half-integer sp ...
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P-symmetry
In physics, a parity transformation (also called parity inversion) is the flip in the sign of ''one'' Three-dimensional space, spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point reflection): \mathbf: \beginx\\y\\z\end \mapsto \begin-x\\-y\\-z\end. It can also be thought of as a test for Chirality (physics), chirality of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image. All fundamental interactions of elementary particles, with the exception of the weak interaction, are symmetric under parity transformation. As established by the Wu experiment conducted at the US National Bureau of Standards by Chinese-American scientist Chien-Shiung Wu, the weak interaction is chiral and thus provides a means for probing chirality in physics. In her experiment, Wu took advantage of the controlling role of weak interactions in radioactive decay of atomic isotopes t ...
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Axiomatic Quantum Field Theory
Axiomatic quantum field theory is a mathematical discipline which aims to describe quantum field theory in terms of rigorous axioms. It is strongly associated with functional analysis and operator algebras, but has also been studied in recent years from a more geometric and functorial perspective. There are two main challenges in this discipline. First, one must propose a set of axioms which describe the general properties of any mathematical object that deserves to be called a "quantum field theory". Then, one gives rigorous mathematical constructions of examples satisfying these axioms. Analytic approaches Wightman axioms The first set of axioms for quantum field theories, known as the Wightman axioms, were proposed by Arthur Wightman in the early 1950s. These axioms attempt to describe QFTs on flat Minkowski spacetime by regarding quantum fields as operator-valued distributions acting on a Hilbert space. In practice, one often uses the Wightman reconstruction theorem, whi ...
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Res Jost
Res Jost (10 January 1918 – 3 October 1990) was a Swiss theoretical physicist, who worked mainly in constructive quantum field theory. Biography Res Jost was born on January 10, 1918, in Bern. He is the son of the physics teacher Wilhelm Jost and Hermine Spycher. In 1949 Jost married the Viennese physicist Hilde Fleischer. Jost studied in Bern and at the University of Zurich, where he received his doctorate in 1946 under the supervision of the German physicist Gregor Wentzel. He then spent half a year with Niels Bohr in Copenhagen, where he introduced the Jost function into scattering theory. Afterwards, he worked as an assistant of Wolfgang Pauli in Zurich. From 1949 to 1955 he was at the Institute for Advanced Study in Princeton, where he worked with Walter Kohn, Joaquin Mazdak Luttinger and Abraham Pais among others. From 1955, he was associate professor for theoretical physics at ETH and starting from 1959 full professor. In 1964, he and Rudolf Haag created the jo ...
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Principle Of Locality
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of instantaneous, or "non-local" action at a distance. Locality evolved out of the Classical field theory, field theories of classical physics. The idea is that for a cause at one point to have an effect at another point, something in the space between those points must mediate the action. To exert an influence, something, such as a wave or particle, must travel through the space between the two points, carrying the influence. The special relativity, special theory of relativity limits the maximum speed at which causal influence can travel to the speed of light, c. Therefore, the principle of locality implies that an event at one point cannot cause a truly simultaneous result at another point. An event at point A cannot cause a result at point B ...
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