Weyl equationIn physics, particularly in quantum field theory, the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles called Weyl fermions. The equation is named after Hermann Weyl. The Weyl fermions are one of the three possible types of elementary fermions, the other two being the Dirac and the Majorana fermions. None of the elementary particles in the Standard Model are Weyl fermions. Previous to the confirmation of the neutrino oscillations, it was considered possible that the neutrino might be a Weyl fermion (it is now expected to be either a Dirac or a Majorana fermion).
Helicity (particle physics)In physics, helicity is the projection of the spin onto the direction of momentum. The angular momentum J is the sum of an orbital angular momentum L and a spin S. The relationship between orbital angular momentum L, the position operator r and the linear momentum (orbit part) p is so L's component in the direction of p is zero. Thus, helicity is just the projection of the spin onto the direction of linear momentum. The helicity of a particle is positive (" right-handed") if the direction of its spin is the same as the direction of its motion and negative ("left-handed") if opposite.
Lie algebra representationIn the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vector space together with a collection of operators on satisfying some fixed set of commutation relations, such as the relations satisfied by the angular momentum operators.
IP PBXAn IP PBX ("Internet Protocol private branch exchange") is a system that connects telephone extensions to the public switched telephone network (PSTN) and provides internal communication for a business. An IP PBX is a PBX system with IP connectivity and may provide additional audio, video, or instant messaging communication utilizing the TCP/IP protocol stack. Voice over IP (VoIP) gateways can be combined with traditional PBX functionality to allow businesses to use their managed intranet to help reduce long distance expenses and take advantage of the benefits of a single network for voice and data (converged network).
Quantum gravityQuantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, such as neutron stars as well as in the early stages of the universe moments after the Big Bang Three of the four fundamental forces of nature are described within the framework of quantum mechanics and quantum field theory: the electromagnetic interaction, the strong force, and the weak force; this leaves gravity as the only interaction that has not been fully accommodated.
Casimir elementIn mathematics, a Casimir element (also known as a Casimir invariant or Casimir operator) is a distinguished element of the center of the universal enveloping algebra of a Lie algebra. A prototypical example is the squared angular momentum operator, which is a Casimir element of the three-dimensional rotation group. More generally, Casimir elements can be used to refer to any element of the center of the universal enveloping algebra. The algebra of these elements is known to be isomorphic to a polynomial algebra through the Harish-Chandra isomorphism.
RotationRotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a axis.
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
Spin representationIn mathematics, the spin representations are particular projective representations of the orthogonal or special orthogonal groups in arbitrary dimension and signature (i.e., including indefinite orthogonal groups). More precisely, they are two equivalent representations of the spin groups, which are double covers of the special orthogonal groups. They are usually studied over the real or complex numbers, but they can be defined over other fields. Elements of a spin representation are called spinors.
Voice over IPVoice over Internet Protocol (VoIP), also called IP telephony, is a method and group of technologies for voice calls, the delivery of voice communication sessions over Internet Protocol (IP) networks, such as the Internet. The broader terms Internet telephony, broadband telephony, and broadband phone service specifically refer to the provisioning of voice and other communications services (fax, SMS, voice messaging) over the Internet, rather than via the public switched telephone network (PSTN), also known as plain old telephone service (POTS).
Brauer's theorem on induced charactersBrauer's theorem on induced characters, often known as Brauer's induction theorem, and named after Richard Brauer, is a basic result in the branch of mathematics known as character theory, within representation theory of a finite group. A precursor to Brauer's induction theorem was Artin's induction theorem, which states that |G| times the trivial character of G is an integer combination of characters which are each induced from trivial characters of cyclic subgroups of G.
Mathematical formulation of quantum mechanicsThe mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces (L2 space mainly), and operators on these spaces.
