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Global symmetry
 
 
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A global symmetry is a symmetry
Symmetry in physics

Symmetry in physics includes all features of a physical system that exhibit the property of symmetry?that is, under certain transformation , aspects of these systems are "unchanged", according to a particular observation....
 that holds for all points in the spacetime
Spacetime

In physics, spacetime is any mathematical model that combines space and Time in physics into a single continuum . Spacetime is usually interpreted with space being Three-dimensional space and time playing the role of a fourth dimension that is of a different sort than the spatial dimensions....
 under consideration, as opposed to a local symmetry that only holds for an open subset of points.

Most physical theories are described by Lagrangian
Lagrangian

The Lagrangian, , of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics known as Lagrangian mechanics....
s which are invariant
Invariance

Invariance is a French journal edited by Jacques Camatte, published since 1968.It emerged from the Italian left-communist tradition associated with Amadeo Bordiga and it originally bore the subtitle "Invariance of the theory of the proletariat", indicating Bordiga's notion of the unchanging nature of communist theory....
 under certain transformations, when the transformations performed at different space-time point
Point (geometry)

In geometry, topology and related branches of mathematics a spatial point describes a specific object within a given space that consists of neither volume, area, length, nor any other higher dimensional analogue....
s are linearly related—they have global symmetries
Symmetry in physics

Symmetry in physics includes all features of a physical system that exhibit the property of symmetry?that is, under certain transformation , aspects of these systems are "unchanged", according to a particular observation....
.

In quantum field theory
Quantum field theory

Quantum field theory or QFT provides a theoretical framework for constructing quantum mechanics models of systems classically described by field or of Many-body problem....
, for example, a global symmetry is any symmetry of a model which is not a gauge symmetry
Gauge symmetry

In gauge symmetry, 'gauge' means 'measure', and symmetry means 'stays the same'. Geometry is the study of the properties of objects that do not change when they move around....
.






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Encyclopedia


A global symmetry is a symmetry
Symmetry in physics

Symmetry in physics includes all features of a physical system that exhibit the property of symmetry?that is, under certain transformation , aspects of these systems are "unchanged", according to a particular observation....
 that holds for all points in the spacetime
Spacetime

In physics, spacetime is any mathematical model that combines space and Time in physics into a single continuum . Spacetime is usually interpreted with space being Three-dimensional space and time playing the role of a fourth dimension that is of a different sort than the spatial dimensions....
 under consideration, as opposed to a local symmetry that only holds for an open subset of points.

Most physical theories are described by Lagrangian
Lagrangian

The Lagrangian, , of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics known as Lagrangian mechanics....
s which are invariant
Invariance

Invariance is a French journal edited by Jacques Camatte, published since 1968.It emerged from the Italian left-communist tradition associated with Amadeo Bordiga and it originally bore the subtitle "Invariance of the theory of the proletariat", indicating Bordiga's notion of the unchanging nature of communist theory....
 under certain transformations, when the transformations performed at different space-time point
Point (geometry)

In geometry, topology and related branches of mathematics a spatial point describes a specific object within a given space that consists of neither volume, area, length, nor any other higher dimensional analogue....
s are linearly related—they have global symmetries
Symmetry in physics

Symmetry in physics includes all features of a physical system that exhibit the property of symmetry?that is, under certain transformation , aspects of these systems are "unchanged", according to a particular observation....
.

In quantum field theory
Quantum field theory

Quantum field theory or QFT provides a theoretical framework for constructing quantum mechanics models of systems classically described by field or of Many-body problem....
, for example, a global symmetry is any symmetry of a model which is not a gauge symmetry
Gauge symmetry

In gauge symmetry, 'gauge' means 'measure', and symmetry means 'stays the same'. Geometry is the study of the properties of objects that do not change when they move around....
. A gauge symmetry is a local symmetry which only allows us to predict the future evolution of a state given its current state up to a gauge transformation. So, a global symmetry is any symmetry, which acting upon any state, never acts to leave the current state invariant but yet changes the future or past state simultaneously.

See also


  • Field (physics)
    Field (physics)

    In physics, a field is a physical quantity associated to each point of spacetime. A field can be classified as a scalar field, a vector field, or a tensor field, according to whether the value of the field at each point is a scalar , a vector , or, more generally, a tensor, respectively....
  • Global spacetime structure
  • Local spacetime structure
    Local spacetime structure

    Local spacetime structure refers to the structure of spacetime on a local level, i.e. only considering those points in an open region of a point....