6.1 Spontaneous symmetry breaking
4 min read•august 1, 2024
Spontaneous symmetry breaking is a key concept in particle physics, explaining how particles acquire mass. It occurs when a system shifts from a symmetric to an asymmetric state without external influence, playing a crucial role in the .
This process is central to the , unifying electromagnetic and weak interactions. It's linked to phase transitions in physical systems and has far-reaching implications for our understanding of fundamental particles and the early universe.
Spontaneous Symmetry Breaking
Concept and Mechanism
Top images from around the web for Concept and Mechanism
Spontaneous symmetry breaking - Wikipedia View original
Is this image relevant?
.png&w=640&q=75)
Higgs boson - Wikipedia View original
Is this image relevant?
Higgs mechanism - Wikipedia View original
Is this image relevant?
Spontaneous symmetry breaking - Wikipedia View original
Is this image relevant?
Higgs boson - Wikipedia View original
Is this image relevant?
1 of 3
Top images from around the web for Concept and Mechanism
Spontaneous symmetry breaking - Wikipedia View original
Is this image relevant?
Higgs boson - Wikipedia View original
Is this image relevant?
Higgs mechanism - Wikipedia View original
Is this image relevant?
Spontaneous symmetry breaking - Wikipedia View original
Is this image relevant?
Higgs boson - Wikipedia View original
Is this image relevant?
1 of 3
- Spontaneous symmetry breaking occurs when a system transitions from a symmetric state to an asymmetric state without external intervention
- Mechanism by which fundamental particles acquire mass in particle physics
- Higgs mechanism exemplifies spontaneous symmetry breaking in the Standard Model
- Associated with phase transitions in physical systems (paramagnetic to ferromagnetic state)
- Vacuum state of can exhibit spontaneous symmetry breaking leading to new particles or interactions
- Goldstone's theorem states every spontaneously broken continuous symmetry produces a massless boson (Goldstone boson)
- In gauge theories, Higgs mechanism allows to be "eaten" by gauge bosons giving them mass
Examples and Applications
- Ferromagnetism demonstrates spontaneous symmetry breaking in condensed matter physics
- Superconductivity involves spontaneous breaking of electromagnetic gauge symmetry
- in quantum chromodynamics explains properties of light mesons
- Electroweak symmetry breaking unifies electromagnetic and weak interactions
- Cosmological inflation theories incorporate spontaneous symmetry breaking to explain early universe expansion
- Nambu-Goldstone modes in liquid crystals result from spontaneous breaking of rotational symmetry
- Bose-Einstein condensation breaks global U(1) symmetry producing coherent quantum state
Potential Energy Function in Symmetry Breaking
Shape and Characteristics
- V(φ) describes energy landscape of physical system in terms of field variables
- Typically has "Mexican hat" or "wine bottle" shape in complex plane for spontaneous symmetry breaking
- Ground state of system corresponds to minimum of potential energy function
- Single minimum at origin indicates symmetric state
- Multiple degenerate minima away from origin signify symmetry breaking
- Choice of particular minimum as vacuum state breaks system symmetry
- Shape determines nature and strength of particle interactions in broken symmetry phase
Mathematical Representation
- Generic form of symmetry-breaking potential:
- μ^2 < 0 and λ > 0 for symmetry-breaking scenario
- Minima occur at
- Expansion around minimum reveals massive and massless modes
- Radial excitations correspond to
- Angular excitations represent Goldstone bosons
- Quantum corrections can modify classical potential (Coleman-Weinberg mechanism)
Consequences of Symmetry Breaking
Particle Masses and Interactions
- Generates mass terms for gauge bosons through interactions with Higgs field
- Explains mass acquisition while photon remains massless
- Fermion masses generated through Yukawa couplings to Higgs field after symmetry breaking
- Particle masses proportional to coupling strengths with Higgs field
- Introduces new interactions (Higgs boson self-interactions, couplings to other particles)
- Broken symmetry phase exhibits different particle spectra and interaction strengths compared to symmetric phase
- Hierarchy problem arises from large difference between weak scale and Planck scale related to symmetry breaking
Phenomenological Implications
- Predicts existence of Higgs boson discovered at Large Hadron Collider in 2012
- Explains origin of electroweak scale and why weak interactions are short-ranged
- Provides mechanism for CP violation in electroweak theory through complex Yukawa couplings
- Affects running of coupling constants and renormalization group flow
- Influences particle decay rates and branching ratios in high-energy collisions
- Shapes thermal history of early universe and phase transitions during cosmic evolution
- Impacts precision electroweak measurements and constrains physics beyond Standard Model
Local vs Global Symmetry Breaking
Characteristics and Differences
- Local symmetry breaking involves gauge symmetries with spacetime-dependent transformation parameters
- Global symmetry breaking involves symmetries with constant transformation parameters across spacetime
- Local symmetry breaking gauge bosons acquire mass through Higgs mechanism
- Global symmetry breaking produces massless Goldstone bosons
- Higgs mechanism exemplifies local symmetry breaking in electroweak theory of Standard Model
- Chiral symmetry breaking in QCD exemplifies global symmetry breaking resulting in pions as pseudo-Goldstone bosons
- Local symmetry breaking preserves gauge invariance crucial for theory renormalizability
Physical Examples and Analogies
- Anderson-Higgs mechanism describes conversion of global to local symmetry breaking in superconductors
- Meissner effect in superconductors analogous to photon in Higgs mechanism
- Josephson effect demonstrates consequences of broken gauge symmetry in superconducting junctions
- Magnetic domains in ferromagnets illustrate spontaneous breaking of rotational symmetry
- Liquid crystals exhibit various phases with different degrees of broken rotational and translational symmetry
- Cosmic strings and domain walls result from global symmetry breaking in early universe
- Baryogenesis theories often involve interplay between local and global symmetry breaking
Key Terms to Review (16)
Chiral symmetry breaking: Chiral symmetry breaking refers to the phenomenon in quantum field theories where a system that possesses a chiral symmetry does not exhibit it in its ground state. This breaking of symmetry has profound implications for particle physics, leading to the emergence of mass for certain particles and affecting the behavior of strongly interacting particles, which ties into concepts like asymptotic freedom and confinement, spontaneous symmetry breaking, and the Higgs mechanism.
Goldstone bosons: Goldstone bosons are massless scalar particles that arise in theories with spontaneously broken continuous symmetries. They represent the degrees of freedom associated with the broken symmetry, and their presence is a fundamental aspect of understanding particle interactions in various physical contexts, including electroweak unification and the Higgs mechanism.
Higgs boson: The Higgs boson is an elementary particle in the Standard Model of particle physics, associated with the Higgs field, which gives mass to other fundamental particles. Its discovery at CERN's Large Hadron Collider in 2012 confirmed the existence of the Higgs field, a crucial aspect of our understanding of mass and particle interactions.
Higgs Mechanism: The Higgs mechanism is a process in particle physics that explains how certain fundamental particles acquire mass through their interaction with the Higgs field. This mechanism is crucial for understanding the origin of mass in the universe and plays a key role in the framework of the Standard Model.
Leonard Susskind: Leonard Susskind is a prominent theoretical physicist known for his significant contributions to string theory, quantum mechanics, and cosmology. He played a crucial role in the development of the holographic principle, which proposes that the information contained within a volume of space can be represented as a theory on the boundary of that space, linking fundamental physics with concepts of symmetry and dimensionality.
LHC Experiments: LHC experiments refer to the scientific investigations conducted at the Large Hadron Collider (LHC), the world’s largest and most powerful particle accelerator located at CERN. These experiments aim to explore fundamental questions about particle physics, such as the nature of the Higgs boson and the existence of dark matter, by colliding protons at high energies to produce a variety of particles and study their interactions.
Mass generation: Mass generation refers to the process by which fundamental particles acquire mass, primarily through interactions with a specific field known as the Higgs field. This phenomenon is essential for explaining why some particles have mass while others remain massless, contributing to the structure of the universe. Mass generation is a core concept in modern particle physics and plays a crucial role in the formulation of the Standard Model, which encompasses our understanding of elementary particles and their interactions.
Particle collisions: Particle collisions refer to interactions between subatomic particles that occur at high energies, where they collide with sufficient force to produce new particles or change their states. These events are crucial for studying the fundamental forces and particles of the universe, revealing insights into the behavior of matter and the laws of physics. Understanding particle collisions also plays a vital role in exploring concepts like mass generation and symmetry breaking.
Peter Higgs: Peter Higgs is a British theoretical physicist who is best known for his work on the Higgs mechanism and the prediction of the Higgs boson. His contributions are fundamental to the Standard Model of particle physics, as they explain how particles acquire mass through spontaneous symmetry breaking, leading to a deeper understanding of the universe's fundamental structure.
Phase Transition: A phase transition is a transformation between different states of matter, such as from solid to liquid or liquid to gas, characterized by changes in physical properties. This phenomenon is often associated with changes in temperature or pressure, leading to the breaking or formation of bonds among particles, which can also have implications in various physical systems, including spontaneous symmetry breaking.
Potential Energy Function: The potential energy function is a mathematical description of the potential energy stored in a system as a function of its configuration or position. It plays a crucial role in various physical theories, especially in explaining how forces interact within a system and how these interactions can lead to changes in state, such as phase transitions and symmetry breaking.
Quantum Field Theory: Quantum Field Theory (QFT) is a fundamental framework in physics that combines classical field theory, special relativity, and quantum mechanics to describe the behavior of subatomic particles and their interactions. It provides the mathematical tools to analyze particle interactions through the use of fields, which permeate space and time, allowing for the creation and annihilation of particles, a key feature that links it to particle interactions, symmetries, and fundamental forces.
Standard Model: The Standard Model is a well-established theoretical framework in particle physics that describes the fundamental particles and their interactions through three of the four known fundamental forces: electromagnetic, weak, and strong forces. It unifies various concepts in particle physics, explaining how particles like quarks and leptons interact through force-carrying particles known as gauge bosons.
Symmetry group: A symmetry group is a mathematical concept that describes the set of all transformations that can be applied to an object without changing its essential properties. In physics, symmetry groups are crucial for understanding the fundamental laws governing particle interactions, as they help define the invariance of physical systems under various transformations, such as rotations and translations.
Vacuum expectation value: The vacuum expectation value (VEV) is the average value of a field in its lowest energy state, or vacuum state, and is a crucial concept in quantum field theory. It signifies the non-zero value that some fields acquire even in the absence of particles, indicating a spontaneous symmetry breaking where the system settles into a state that is not symmetric under certain transformations. The existence of a VEV leads to various physical phenomena, such as mass generation for particles through interactions with these fields.
W and Z Bosons: W and Z bosons are fundamental particles that mediate the weak nuclear force, one of the four fundamental forces of nature. These particles are crucial for processes like beta decay in atomic nuclei, making them key players in particle physics. They arise from the electroweak theory, which unifies the electromagnetic force and the weak nuclear force, and their existence is a vital aspect of the Standard Model.