We show that the relativistic matter waves of two particle system contains the SU(2) symmetry; the relativistic matter waves of three particle system contains the SU(3) symmetry. Therefore, the relativistic matter wave is suitable for describing many-particle system such as quarks or gluons etc that are engaged with implicated symmetry problems. The weak interaction and strong interaction are investigated by using the relativistic de Broglie matter wave with SU(n) symmetry. Our results agree well with experiments. This work is to re-discover and re-explore de Broglie matter wave with the SU(n) symmetry and its applications to particle physics. This work was divided into two parts: Chapter 1, Relativistic de Broglie matter wave; Chapter 2, Factory of prosthesis.We show that the relativistic matter waves of two particle system contains the SU(2) symmetry; the relativistic matter waves of three particle system contains the SU(3) symmetry. Therefore, the relativistic matter wave is suitable for describing many-particle system such as quarks or gluons etc that are engaged with implicated symmetry problems. The weak interaction and strong interaction are investigated by using the relativistic de Broglie matter wave with SU(n) symmetry. Our results agree well with experiments. This work is to re-discover and re-explore de Broglie matter wave with the SU(n) symmetry and its applications to particle physics. This work was divided into two parts: Chapter 1, Relativistic de Broglie matter wave; Chapter 2, Factory of prosthesis.

arXiv:1806.02159May 30, 20180 citations

Breaking symmetry

Noriaki Horiuchi

Nature PhotonicsFeb 19, 20180 citations

Symmetry

Detlef Dürr, Stefan Teufel

Springer eBooksJan 1, 20090 citations

Emergent anomalous higher symmetries from topological order and from dynamical electromagnetic field in condensed matter systems

Xiao-Gang Wen

Global symmetry (0-symmetry) acts on the whole space while higher $k$ -symmetry acts on all the codimension- $k$ closed subspaces. The usual condensed matter lattice theories do not include dynamical electromagnetic (EM) field and do not have higher symmetries (unless we engineer fine-tuned toy models). However, for gapped systems, (anomalous) higher symmetries can emerge from the usual condensed matter theories at low energies (usually in a spontaneously broken form). We pointed out that the emergent spontaneously broken higher symmetries are nothing but a kind of topological order. Thus the study of emergent spontaneously broken higher symmetries is a study of topological order. The emergent (anomalous) higher symmetries can be used to constrain possible phase transitions and possible phases induced by certain types of excitations in topological orders. (Anomalous) higher symmetry can also emerge in gapless systems if the gapless excitations contain gapless gauge fields. In particular, EM condensed matter systems that include the dynamical EM field have an emergent anomalous $U(1)$ -1-symmetry below the energy gap of the magnetic monopoles. So EM condensed matter systems can realize some physical phenomena of anomalous higher symmetry. In particular, any gapped liquid phase of an EM condensed matter system (induced by arbitrary fluctuations and condensations of electric charges and photons) must have a nontrivial bosonic topological order.Global symmetry (0-symmetry) acts on the whole space while higher $k$-symmetry acts on all the codimension-$k$ closed subspaces. The usual condensed matter lattice theories do not include dynamical electromagnetic (EM) field and do not have higher symmetries (unless we engineer fine-tuned toy models). However, for gapped systems, (anomalous) higher symmetries can emerge from the usual condensed matter theories at low energies (usually in a spontaneously broken form). We pointed out that the emergent spontaneously broken higher symmetries are nothing but a kind of topological order. Thus the study of emergent spontaneously broken higher symmetries is a study of topological order. The emergent (anomalous) higher symmetries can be used to constrain possible phase transitions and possible phases induced by certain types of excitations in topological orders. (Anomalous) higher symmetry can also emerge in gapless systems if the gapless excitations contain gapless gauge fields. In particular, EM condensed matter systems that include the dynamical EM field have an emergent anomalous $U(1)$-1-symmetry below the energy gap of the magnetic monopoles. So EM condensed matter systems can realize some physical phenomena of anomalous higher symmetry. In particular, any gapped liquid phase of an EM condensed matter system (induced by arbitrary fluctuations and condensations of electric charges and photons) must have a nontrivial bosonic topological order.

arXiv:1812.02517Physical review. B./Physical review. BMay 22, 2019127 citations

Choreographed entanglement dances: Topological states of quantum matter

Xiao-Gang Wen

It has long been thought that all different phases of matter arise from symmetry breaking. Without symmetry breaking, there would be no pattern, and matter would be featureless. However, it is now clear that for quantum matter at zero temperature, even symmetric disordered liquids can have features, giving rise to topological phases of quantum matter. Some of the topological phases are highly entangled (that is, have topological order), whereas others are weakly entangled (that is, have symmetry-protected trivial order). This Review provides a brief summary of these zero-temperature states of matter and their emergent properties, as well as their importance in unifying some of the most basic concepts in nature.It has long been thought that all different phases of matter arise from symmetry breaking. Without symmetry breaking, there would be no pattern, and matter would be featureless. However, it is now clear that for quantum matter at zero temperature, even symmetric disordered liquids can have features, giving rise to topological phases of quantum matter. Some of the topological phases are highly entangled (that is, have topological order), whereas others are weakly entangled (that is, have symmetry-protected trivial order). This Review provides a brief summary of these zero-temperature states of matter and their emergent properties, as well as their importance in unifying some of the most basic concepts in nature.

arXiv:1906.05983ScienceFeb 22, 2019171 citations

Johannes Hecker Denschlag

NatureJul 25, 20071 citation

Global symmetry (0-symmetry) acts on the whole space while higher

k

-symmetry acts on all the codimension-

k

closed subspaces. The usual condensed matter lattice theories do not include dynamical electromagnetic (EM) field and do not have higher symmetries (unless we engineer fine-tuned toy models). However, for gapped systems, (anomalous) higher symmetries can emerge from the usual condensed matter theories at low energies (usually in a spontaneously broken form). We pointed out that the emergent spontaneously broken higher symmetries are nothing but a kind of topological order. Thus the study of emergent spontaneously broken higher symmetries is a study of topological order. The emergent (anomalous) higher symmetries can be used to constrain possible phase transitions and possible phases induced by certain types of excitations in topological orders. (Anomalous) higher symmetry can also emerge in gapless systems if the gapless excitations contain gapless gauge fields. In particular, EM condensed matter systems that include the dynamical EM field have an emergent anomalous

U(1)

-1-symmetry below the energy gap of the magnetic monopoles. So EM condensed matter systems can realize some physical phenomena of anomalous higher symmetry. In particular, any gapped liquid phase of an EM condensed matter system (induced by arbitrary fluctuations and condensations of electric charges and photons) must have a nontrivial bosonic topological order.