{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-c03aa079.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-517835be.css\" media=\"all\" /\u003e\n\u003cdiv data-title='Gauge Theory Made Simple: How Symmetry Works in Quantum Physics' data-url='/boclips/videos/689566e78b3f8d9d4df8e337' data-video-url='/boclips/videos/689566e78b3f8d9d4df8e337' id='bo_player_modal'\u003e\n\u003cdiv class='boclips-resource-page modal-dialog panel-container'\u003e\n\u003cdiv class='react-notifications-root'\u003e\u003c/div\u003e\n\u003cdiv class='rp-header'\u003e\n\u003cdiv class='rp-type'\u003e\n\u003ci aria-hidden='true' class='fai fa-regular fa-circle-play'\u003e\u003c/i\u003e\nVideo\n\u003c/div\u003e\n\u003ch1 class='rp-title' id='video-title'\u003e\nGauge Theory Made Simple: How Symmetry Works in Quantum Physics\n\u003c/h1\u003e\n\u003cdiv class='rp-actions'\u003e\n\u003cdiv class='mr-1'\u003e\n\u003ca class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"\u003e\u003cspan\u003e\u003cspan\u003eGet Free Access\u003c/span\u003e\u003cspan class=\"\"\u003e for 10 Days\u003c/span\u003e\u003cspan\u003e!\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-body'\u003e\n\u003cdiv class='rp-info'\u003e\n\u003cdiv aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'\u003e\u0026times;\u003c/div\u003e\n\u003ci aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003ci aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003cdiv class='rp-rating'\u003e\n\u003cspan class='resource-pool'\u003e\n\u003cspan class='pool-label'\u003ePublisher:\u003c/span\u003e\n\u003cspan class='pool-name'\u003e\n\u003cspan class='text'\u003e\u003ca data-publisher-id=\"30356011\" href=\"/search?publisher_ids%5B%5D=30356011\"\u003eCurated Video\u003c/a\u003e\u003c/span\u003e\n\u003c/span\u003e\n\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-description'\u003e\n\u003cspan class='short-description'\u003eIf you ask a physicist, what is at the core of physics, you will hear symmetry.  What is symmetry? Gauge theory explained simply. Symmetry is about actions that don't change anything. If we take an equilateral triangle, and put a mirror...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eIf you ask a physicist, what is at the core of physics, you will hear symmetry.  What is symmetry? Gauge theory explained simply. \u003cbr/\u003e\u003cbr/\u003eSymmetry is about actions that don't change anything. If we take an equilateral triangle, and put a mirror from one corner to the middle of the opposite side, we will see that the whole triangle. This is a symmetry of the equilateral triangle. Similarly we can rotate the triangle by 120 degrees, and it will look identical to what it was before. \u003cbr/\u003e\u003cbr/\u003eWhat we just did is a simple example of something more complex - group theory. Group theory is the math behind the symmetries.The mathematics behind the symmetries of the equilateral triangle is called the dihedral GROUP of degree 3, where 3 refers to the triangle having three corners. We can change the elements, or permutations, using two different operations, rotation, and reflection. These two operations are called generators. The result of applying a generator doesn’t change anything visible. This is symmetry. \u003cbr/\u003e\u003cbr/\u003eSymmetries give us rules for how to transform something while conserving a quantity. For the triangle, that conserved quantity is its shape, and the generators are rotation and reflection. \u003cbr/\u003e\u003cbr/\u003eThis leads us to Noether’s theorem which states that “For every symmetry there is a corresponding conservation law.” This directly connects symmetries with conserved quantities. \u003cbr/\u003e\u003cbr/\u003eWhat happens if we take the limit of a polygon with an infinite number of edges? We get a circle. A circle of some radius, r, can be described on a 2D plane using polar coordinates by two equations. If we use complex numbers to represent the circle, we can write it with just ONE equation. This allows us to write one complex equation that achieves the same mathematically as two real equations. \u003cbr/\u003e\u003cbr/\u003eIt turns out that there’s also a symmetry group associated with this circle of complex numbers with a radius or magnitude of 1. It is called the U(1) group. The elements of the group are all the infinite possible angles phi around the circle. \u003cbr/\u003e\u003cbr/\u003eQuantum mechanics is built on complex numbers. We can apply the symmetry with the simple transformation of moving around the circle. Do described the movement of fermions, we can use the Dirac equation. It describes any matter particle, like an electron, with some mass m moving in space. It does not describe any forces. \u003cbr/\u003e\u003cbr/\u003eIf U(1) symmetry exists, it would mean that if we applied our transformation, the Lagrangian would not change. The problem is that the Lagrangian DOES change when we apply this transformation, so this tells us that no U(1) symmetry exists.\u003cbr/\u003e\u003cbr/\u003eHowever, if we modify the equation, by adding a new quantum field to the theory, a gauge field, we can get a symmetry. Another name for a gauge field is a force. Our theory works, and obeys U(1) symmetry transformations if we add some new terms to the equation. It turns out that this new term describes the electromagnetic force. The entire theory of Quantum Electrodynamics can be derived by the new transformed equation.\u003cbr/\u003e\u003cbr/\u003eSo by taking a theory for fermions (Dirac equation) and demanding a U(1) transformation we got the theory of electromagnetism. Similarly, the standard model is constructed to respect three symmetries or special unitary groups. And each group leads to a symmetry resulting in a conservation law and a fundamental force. \u003cbr/\u003e\u003cbr/\u003eThe U(1) group gives us conservation of electric charge, and is associated with the electromagnetic force. The SU(2) group gives us conservation of weak isospin, or weak charge, and is associated with the weak force. The SU(3) group leads to conservation of color charge and is associated with the strong force. It leads to the theory of quantum chromodynamics.\u003cbr/\u003e\u003cbr/\u003eIn addition, the number of generators corresponds to the number of bosons involved with each force. U(1) has one generator and one photon. SU(2) has 3 generators and 3 W+, W-, and Z. SU(3) has 8 generators and 8 different gluons. \u003cbr/\u003eSymmetries seem to be the foundation of the laws of physics. 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