Qhov sib txawv tseem ceeb ntawm Lorentz ntsuas thiab Coulomb ntsuas yog qhov ntsuas Lorentz muaj feem cuam tshuam rau Minkowski qhov chaw, qhov ntsuas Coulomb cuam tshuam nrog Euclidean qhov chaw.
Feem ntau, Minkowski qhov chaw yog 4D (plaub-dimensional) qhov chaw vector tiag tiag. Qhov no yog txawm peem rau nrog ib tug nondegenerate, symmetric bilinear daim ntawv. Nws kuj tshwm sim ntawm qhov chaw tangent ntawm txhua qhov chaw hauv lub sijhawm. Qhov chaw Euclidean, ntawm qhov tod tes, yog ib qho tseem ceeb hauv classical geometry. Nws yog 3D (peb-dimensional) qhov chaw.
Lorentz Gauge yog dab tsi?
Lorentz gauge yog ib feem gauge kho ntawm electromagnetic vector peev xwm. Lub tswv yim no tau piav qhia thawj zaug los ntawm Ludwig Lorenz. Lo lus no feem ntau muaj nws cov ntawv thov hauv electromagnetism. Feem ntau, peb tuaj yeem siv Lorentz gauge hauv electromagnetism rau kev xam cov sij hawm-nyob ntawm electromagnetic teb los ntawm cov muaj feem cuam tshuam.
Daim duab 01: Minkowski Space
Keeb kwm, thaum ua haujlwm ntawm Ludwig Lorenz tau luam tawm, Maxwell tsis tau txais qhov zoo. Tom qab ntawd, nws tshem tawm Coulomb electrostatic quab yuam los ntawm nws qhov kev sib npaug ntawm electromagnetic yoj sib npaug. Qhov no yog vim nws tau ua haujlwm hauv Coulomb ntsuas. Qhov tseem ceeb tshaj, qhov ntsuas Lorentz cuam tshuam nrog Minkowski qhov chaw.
Coulomb Gauge yog dab tsi?
Coulomb gauge yog ib hom kev ntsuas uas tau qhia nyob rau hauv cov nqe lus ntawm instantaneous qhov tseem ceeb ntawm cov teb thiab ceev. Nws tseem hu ua transverse gauge. Lub tswv yim no muaj txiaj ntsig zoo hauv quantum chemistry thiab condensed teeb meem physics. Peb tuaj yeem txhais nws siv qhov ntsuas ntsuas, lossis ntau dua, siv qhov ntsuas ntsuas kho qhov xwm txheej.
Qhov ntsuas Coulomb no tshwj xeeb tshaj yog muaj txiaj ntsig hauv kev suav ib nrab classic uas tuaj hauv quantum mechanics. Ntawm no, lub peev xwm vector yog quantized, tab sis Coulomb kev sib cuam tshuam tsis yog. Hauv Coulomb ntsuas, peb tuaj yeem nthuav qhia qhov muaj peev xwm ntawm cov txiaj ntsig tam sim ntawm cov teb thiab qhov ntom ntom.
Daim duab 02: Euclidean Space
Ntxiv mus, kev ntsuas kev hloov pauv tuaj yeem khaws cov kev ntsuas Coulomb, uas tuaj yeem tsim nrog ntsuas kev ua haujlwm uas txaus siab rau lub tswv yim. Txawm li cas los xij, hauv cov cheeb tsam uas nyob deb ntawm cov nqi hluav taws xob ntawm lub peev xwm scalar, Coulomb ntsuas tau dhau los ua xoom, thiab peb hu nws lub ntsuas hluav taws xob. Qhov hluav taws xob hluav taws xob hluav taws xob no yog thawj zaug hauv qhov ntsuas no.
Tsis tas li ntawd, Coulomb gauge lees txais lub ntuj tsim Hamiltonian ntawm cov evolution equations (txog cov electromagnetic teb) ntawm electromagnetic teb interacting nrog ib tug conserved tam sim no. Qhov no yog qhov zoo ntawm qhov quantization ntawm txoj kev xav. Qhov tseem ceeb tshaj, Coulomb gauge muaj feem xyuam rau qhov chaw Euclidean.
Qhov txawv ntawm Lorentz Gauge thiab Coulomb Gauge yog dab tsi?
Lorentz gauge thiab Coulomb gauge yog ob lub ntsiab lus tseem ceeb hauv quantum chemistry. Lorentz gauge yog ib feem gauge kho ntawm electromagnetic vector muaj peev xwm thaum Coulomb gauge yog ib hom kev ntsuas uas tau qhia nyob rau hauv cov nqe lus ntawm instantaneous qhov tseem ceeb ntawm cov teb thiab ceev. Qhov sib txawv tseem ceeb ntawm Lorentz gauge thiab Coulomb gauge yog tias Lorentz gauge muaj feem xyuam rau Minkowski qhov chaw, whereas Coulomb gauge muaj feem xyuam rau Euclidean qhov chaw. Minkowski qhov chaw yog 4D (plaub-dimensional) qhov chaw vector tiag tiag, thaum Euclidean qhov chaw yog 3 D (peb-dimensional) qhov chaw, uas tseem yog qhov tseem ceeb ntawm classical geometry.
Hauv qab no yog cov ntsiab lus ntawm qhov sib txawv ntawm Lorentz gauge thiab Coulomb gauge hauv daim ntawv tabular rau ib sab ntawm kev sib piv.
Summary – Lorentz Gauge vs Coulomb Gauge
Peb tuaj yeem paub qhov txawv ntawm Lorentz gauge thiab Mikowskin gauge nyob ntawm qhov ntev. Qhov sib txawv tseem ceeb ntawm Lorentz gauge thiab Coulomb gauge yog Lorentz gauge muaj feem xyuam rau Minkowski qhov chaw, whereas Coulomb gauge muaj feem xyuam rau Euclidean qhov chaw. Minkowski qhov chaw yog 4D (plaub-dimensional) qhov chaw vector tiag tiag, thaum Euclidean qhov chaw yog qhov tseem ceeb ntawm cov geometry classical thiab yog 3 D (peb-dimensional) qhov chaw.
