Fundamental where a canonical example is a

Fundamental physics seeks to answer challengingquestions facing human beings regarding their universe.  Past analytical approaches have focused onprecision experiments involving abstract theoretical reasoning and incorporatedcurrent findings on building blocks of nature. One of the fundamental principle identified is that universe is formedby matter that is under the influence of significant forces.  The first three primary effects areelectromagnetism, strong nuclear force, and weak nuclear force.  These forces are described using the StandardModel of particle physics that also highlights all known matter particles bothleptons and quarks that combine to form composite particles that we observe.  According to the Standard Model, all mattertypes and forces are defined by the fields filling all the space-time.  These relationships are well represented inequations that define these fields relating to effects of relativity andquantum mechanics where Standard Model (SM) is part of quantum field theory(QFT).

  The particles exist as quanta ofthe fields where a canonical example is a photon (representing quantum of electromagneticfields).  Additionally, the fieldscontain abstract mathematical symmetries making QFT also referred to as a (none)-Abeliangauge theory.  These terms are defined inparagraphs that follow.After the three forces described above does GeneralTheory of Relativity (GR) explain the gravity, which is best.  Therefore, time and space are dynamic and notstatic upon which the particles and forces operate.  GR equations prove that energy and matterwarp the fabric of spacetime in a pathway that is prescribed where thecurvature is identified by gravitational force. The analogy of how the curvature produces an attractive force is asshown in figure 1 below.

  The figureshows a curved space with observers A and B who are walking towards the NorthPole (N).  A and B start off mutuallyparallel, where due to curvature, they tend to move towards each other,illustrating a form of attractiveness. General Theory of Relativity (GR) underpins theunderstanding working of the universe at large scales.  Therefore, black holes may exist where theworld could have expanded outwards due to effects of ‘big bang’ in the pastwithin a finite time.  Additionally, theGeneral Theory of Relativity (GR) allows supporting the existence ofgravitational waves representing ripples in the fabric of the space-time, whichare analogous to the wave-like solutions in Maxwell’s equation ofelectromagnetism.  On a practical levelis the curvature of spacetime that is sited through satellite communications.  GR is, therefore, part of our daily lifeusing the positioning systems of smartphones.

Despite advancement in studies on SM and GR, there aremany puzzling questions.  For instance,one could find it difficult to understand how only four fundamental forcesexist and why the matter has particular properties such as charge and massconcerning each of the forces.  Anotherconcern is that classical theory of GR breaks down at extreme points in thespacetime like the center of the big bang or black hole.  In such cases, a curvature of the spacetimeis infinite (not physically sensible).  Therefore,theorists in physics believe that SM and GR form part of the broadertheoretical framework that includes quantum effects relating to gravitationalforce in line with other forces.

  The GRis turned into quantum field theory where gravity is carried by graviton whilethe photon carries electromagnetic force in SM. Quantum gravity solvesinability of the GR to describe the black hole physics, dark energy, or bigbang.  One of the main challenges isinvestigating quantum gravity where there is sheer complexity in calculations.To understanding the interaction between SM and GR,understanding of double copy is critical. It relates to the quantities that are calculated in gauge theory, wheresimilar quantities can be obtained from the gravity theory.  The original form for this correspondencerequires understanding of scattering amplitudes where complex-valued functionsof momenta that relate to the probability of a particular set of particlesinteract.

  However, the discussionintroduces other than gauge and gravity theories to include standard solutionssuch as the black holes.  Additionally,other similar correspondences occur between different field theory typeswhether or not they have supersymmetry.  Thedouble copy gives the potential for physicists to understand gravity takinginto account that it relates to theories such as SM where the quantum behaviouris well known with gravity. One should note that if one thinks of gravity in theright approach, it could be more straightforward in comparison to othertraditional calculators demonstrated in GR. This opens up an understanding of the gauge theory.  In double copy approach, there are scatteringamplitudes between gravity and gauge theories. Results of gauge theory are written in a way that they obey intriguingsymmetry between parts relating to their momenta, polarisations, and elementsthat relates charges in each of the gluons, which is known as the BCJ dualityusually imply that various degrees of freedom are closely related thanpreviously thought.

  It is important tostudy the gauge theories in details as explained in following sections todefine double copy in a better way.